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Номер 714, страница 193 - гдз по алгебре 9 класс учебник Макарычев, Миндюк
Авторы: Макарычев Ю. Н., Миндюк Н. Г., Нешков К. И., Суворова С. Б.
Тип: Учебник
Издательство: Просвещение
Год издания: 2023 - 2026
Уровень обучения: базовый
Цвет обложки: белый, зелёный, фиолетовый
ISBN: 978-5-09-112135-3
Допущено Министерством просвещения Российской Федерации
Популярные ГДЗ в 9 классе
Глава 5. Арифметическая и геометрическая прогрессии. Параграф 10. Геометрическая прогрессия. Упражнения для повторения курса 7-9 классов - номер 714, страница 193.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 171903 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "193" "field_page_end" => null "field_url" => "/9-klass/algebra/makarychev-fgos/714" "field_display_title" => "714" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1080 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 171142 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Арифметическая и геометрическая прогрессии" "field_branch_order" => "5" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_page_start" => "149" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 171142 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Арифметическая и геометрическая прогрессии" "field_branch_order" => "5" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "149" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1077} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1289 #items: array:3 [ 0 => App\Models\Branch {#1078 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 171142 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Арифметическая и геометрическая прогрессии" "field_branch_order" => "5" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1081 #items: array:1 [ 0 => App\Models\Term {#1079 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_page_start" => "149" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Book {#1083 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1119 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 171142 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Арифметическая и геометрическая прогрессии" "field_branch_order" => "5" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1081} "field_page_start" => "149" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1082} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1119} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1120 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 171148 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Геометрическая прогрессия" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 0 => App\Models\Term {#1122 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_page_start" => "167" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Book {#1124 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ 0 => App\Models\Branch {#1161 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 171148 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Геометрическая прогрессия" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121} "field_page_start" => "167" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1123} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1160} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1202 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 171154 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения для повторения курса 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1203 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "188" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:1 [ 0 => App\Models\Book {#1205 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1241 #items: array:1 [ 0 => App\Models\Branch {#1242 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 171154 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения для повторения курса 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1203} "field_page_start" => "188" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1204} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1241} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1288 #items: array:8 [ 0 => App\Models\Element {#1305 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 179204 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1314 #items: array:1 [ 0 => App\Models\Edition {#1306 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171903" "type" => "task" ] "text" => """ <p><strong>714</strong>. Упростите выражение:</p><figure><figure>\n <img src="/media/algebra_09/makarychev-2023/0-00/714.webp?ts=1744127448" alt="Упражнение 714 упростить выражение" loading="lazy" width="1347" height="293">\n </figure>\n <figcaption> </figcaption></figure> """ "img" => array:1 [ 0 => array:5 [ "name" => "714-1.jpg" "alt" => null "width" => "1574" "height" => 311 "path" => "/media/algebra_09/makarychev-2023/0-00/714-1.webp?ts=1734090952" ] ] ] #original: array:7 [ "id" => 179204 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1314} "task" => array:2 [ "refs" => "171903" "type" => "task" ] "text" => """ <p><strong>714</strong>. Упростите выражение:</p><figure><figure>\n <img src="/media/algebra_09/makarychev-2023/0-00/714.webp?ts=1744127448" alt="Упражнение 714 упростить выражение" loading="lazy" width="1347" height="293">\n </figure>\n <figcaption> </figcaption></figure> """ "img" => array:1 [ 0 => array:5 [ "name" => "714-1.jpg" "alt" => null "width" => "1574" "height" => 311 "path" => "/media/algebra_09/makarychev-2023/0-00/714-1.webp?ts=1734090952" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1312 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 180197 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1322 #items: array:1 [ 0 => App\Models\Edition {#1313 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171903" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "714-1.jpg" "alt" => null "width" => "1670" "height" => 1637 "path" => 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+timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171903" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "714-1.png" "alt" => null "width" => "650" "height" => 496 "path" => "/media/algebra_09/makarychev-2023/3-00/714-1.webp?ts=1734091912" ] ] ] #original: array:6 [ "id" => 181562 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1338} "task" => array:2 [ "refs" => "171903" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "714-1.png" "alt" => null "width" => "650" "height" => 496 "path" => "/media/algebra_09/makarychev-2023/3-00/714-1.webp?ts=1734091912" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: 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#hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Element {#1344 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 182993 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1354 #items: array:1 [ 0 => App\Models\Edition {#1345 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: 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#hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Element {#1352 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 184149 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1362 #items: array:1 [ 0 => App\Models\Edition {#1353 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171903" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "714-1.jpg" "alt" => null "width" => "1575" "height" => 735 "path" => "/media/algebra_09/makarychev-2023/7-00/714-1.webp?ts=1734093500" ] ] ] #original: array:6 [ "id" => 184149 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1362} "task" => array:2 [ "refs" => "171903" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "714-1.jpg" "alt" => null "width" => "1575" "height" => 735 "path" => "/media/algebra_09/makarychev-2023/7-00/714-1.webp?ts=1734093500" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 7 => App\Models\Element {#1360 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1349553 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1370 #items: array:1 [ 0 => App\Models\Edition {#1361 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171903" "type" => "task" ] "text" => "<p><strong>а)</strong> $(4x^{-2}y^3)^2 \cdot (0.5x^2y^{-1})^3$</p><p>Чтобы упростить выражение, сначала возведем каждый множитель в соответствующую степень, используя правила $(ab)^n = a^n b^n$ и $(a^m)^n = a^{mn}$:</p><p>$(4x^{-2}y^3)^2 = 4^2 \cdot (x^{-2})^2 \cdot (y^3)^2 = 16x^{-4}y^6$</p><p>$(0.5x^2y^{-1})^3 = (0.5)^3 \cdot (x^2)^3 \cdot (y^{-1})^3 = 0.125x^6y^{-3}$</p><p>Теперь перемножим полученные выражения, группируя коэффициенты и переменные с одинаковыми основаниями:</p><p>$(16x^{-4}y^6) \cdot (0.125x^6y^{-3}) = (16 \cdot 0.125) \cdot (x^{-4}x^6) \cdot (y^6y^{-3})$</p><p>Используя правило $a^m \cdot a^n = a^{m+n}$, завершим упрощение:</p><p>$2 \cdot x^{-4+6} \cdot y^{6+(-3)} = 2x^2y^3$</p><p>Ответ: $2x^2y^3$</p><p><strong>б)</strong> $(\frac{c^4}{6x^2y^{-5}})^{-2} \cdot (\frac{1}{3}c^2x^3y^{-2})^4$</p><p>Для первого множителя применим свойство $(\frac{a}{b})^{-n} = (\frac{b}{a})^n$. Для второго — свойство $(abc)^n = a^n b^n c^n$.</p><p>$(\frac{c^4}{6x^2y^{-5}})^{-2} = (\frac{6x^2y^{-5}}{c^4})^2 = \frac{6^2(x^2)^2(y^{-5})^2}{(c^4)^2} = \frac{36x^4y^{-10}}{c^8}$</p><p>$(\frac{1}{3}c^2x^3y^{-2})^4 = (\frac{1}{3})^4(c^2)^4(x^3)^4(y^{-2})^4 = \frac{1}{81}c^8x^{12}y^{-8}$</p><p>Теперь перемножим полученные выражения:</p><p>$\frac{36x^4y^{-10}}{c^8} \cdot \frac{1}{81}c^8x^{12}y^{-8} = \frac{36}{81} \cdot \frac{c^8}{c^8} \cdot (x^4x^{12}) \cdot (y^{-10}y^{-8})$</p><p>Сократим дробь $\frac{36}{81}$ на 9 и сложим показатели степеней:</p><p>$\frac{4}{9} \cdot 1 \cdot x^{4+12} \cdot y^{-10-8} = \frac{4}{9}x^{16}y^{-18}$</p><p>Ответ: $\frac{4}{9}x^{16}y^{-18}$</p><p><strong>в)</strong> $(0.25a^{-3}b^4)^{-2} \cdot (2a^5b^{-6})^{-1}$</p><p>Представим $0.25$ как $\frac{1}{4}$ и применим свойства степеней:</p><p>$(0.25a^{-3}b^4)^{-2} = (\frac{1}{4})^{-2}(a^{-3})^{-2}(b^4)^{-2} = 4^2 a^{6} b^{-8} = 16a^6b^{-8}$</p><p>$(2a^5b^{-6})^{-1} = 2^{-1}(a^5)^{-1}(b^{-6})^{-1} = \frac{1}{2}a^{-5}b^6$</p><p>Перемножим результаты:</p><p>$(16a^6b^{-8}) \cdot (\frac{1}{2}a^{-5}b^6) = (16 \cdot \frac{1}{2}) \cdot (a^6a^{-5}) \cdot (b^{-8}b^6)$</p><p>Упростим, выполнив умножение коэффициентов и сложение показателей степеней:</p><p>$8 \cdot a^{6-5} \cdot b^{-8+6} = 8a^1b^{-2} = 8ab^{-2}$</p><p>Ответ: $8ab^{-2}$</p><p><strong>г)</strong> $(\frac{0.1a^{-2}}{b^{-1}c^3})^5 \cdot (\frac{b^5}{10a^4c^6})^{-3}$</p><p>Применим свойство $(\frac{a}{b})^{-n} = (\frac{b}{a})^n$ ко второму множителю. Заметим, что $0.1 = \frac{1}{10} = 10^{-1}$.</p><p>$(\frac{10^{-1}a^{-2}}{b^{-1}c^3})^5 \cdot (\frac{10a^4c^6}{b^5})^3$</p><p>Возведем каждую дробь в соответствующую степень:</p><p>$\frac{(10^{-1})^5(a^{-2})^5}{(b^{-1})^5(c^3)^5} \cdot \frac{10^3(a^4)^3(c^6)^3}{(b^5)^3} = \frac{10^{-5}a^{-10}}{b^{-5}c^{15}} \cdot \frac{10^3a^{12}c^{18}}{b^{15}}$</p><p>Перемножим дроби, сгруппировав подобные члены:</p><p>$\frac{(10^{-5} \cdot 10^3) \cdot (a^{-10}a^{12}) \cdot c^{18}}{(b^{-5}b^{15}) \cdot c^{15}} = \frac{10^{-2} \cdot a^{-10+12} \cdot c^{18}}{b^{-5+15} \cdot c^{15}} = \frac{10^{-2}a^2c^{18}}{b^{10}c^{15}}$</p><p>Применим свойство $\frac{a^m}{a^n} = a^{m-n}$ для переменной $c$:</p><p>$\frac{10^{-2}a^2c^{18-15}}{b^{10}} = \frac{10^{-2}a^2c^3}{b^{10}} = \frac{a^2c^3}{100b^{10}}$</p><p>Ответ: $\frac{a^2c^3}{100b^{10}}$</p>" ] #original: array:6 [ "id" => 1349553 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1370} "task" => array:2 [ "refs" => "171903" "type" => "task" ] "text" => "<p><strong>а)</strong> $(4x^{-2}y^3)^2 \cdot (0.5x^2y^{-1})^3$</p><p>Чтобы упростить выражение, сначала возведем каждый множитель в соответствующую степень, используя правила $(ab)^n = a^n b^n$ и $(a^m)^n = a^{mn}$:</p><p>$(4x^{-2}y^3)^2 = 4^2 \cdot (x^{-2})^2 \cdot (y^3)^2 = 16x^{-4}y^6$</p><p>$(0.5x^2y^{-1})^3 = (0.5)^3 \cdot (x^2)^3 \cdot (y^{-1})^3 = 0.125x^6y^{-3}$</p><p>Теперь перемножим полученные выражения, группируя коэффициенты и переменные с одинаковыми основаниями:</p><p>$(16x^{-4}y^6) \cdot (0.125x^6y^{-3}) = (16 \cdot 0.125) \cdot (x^{-4}x^6) \cdot (y^6y^{-3})$</p><p>Используя правило $a^m \cdot a^n = a^{m+n}$, завершим упрощение:</p><p>$2 \cdot x^{-4+6} \cdot y^{6+(-3)} = 2x^2y^3$</p><p>Ответ: $2x^2y^3$</p><p><strong>б)</strong> $(\frac{c^4}{6x^2y^{-5}})^{-2} \cdot (\frac{1}{3}c^2x^3y^{-2})^4$</p><p>Для первого множителя применим свойство $(\frac{a}{b})^{-n} = (\frac{b}{a})^n$. Для второго — свойство $(abc)^n = a^n b^n c^n$.</p><p>$(\frac{c^4}{6x^2y^{-5}})^{-2} = (\frac{6x^2y^{-5}}{c^4})^2 = \frac{6^2(x^2)^2(y^{-5})^2}{(c^4)^2} = \frac{36x^4y^{-10}}{c^8}$</p><p>$(\frac{1}{3}c^2x^3y^{-2})^4 = (\frac{1}{3})^4(c^2)^4(x^3)^4(y^{-2})^4 = \frac{1}{81}c^8x^{12}y^{-8}$</p><p>Теперь перемножим полученные выражения:</p><p>$\frac{36x^4y^{-10}}{c^8} \cdot \frac{1}{81}c^8x^{12}y^{-8} = \frac{36}{81} \cdot \frac{c^8}{c^8} \cdot (x^4x^{12}) \cdot (y^{-10}y^{-8})$</p><p>Сократим дробь $\frac{36}{81}$ на 9 и сложим показатели степеней:</p><p>$\frac{4}{9} \cdot 1 \cdot x^{4+12} \cdot y^{-10-8} = \frac{4}{9}x^{16}y^{-18}$</p><p>Ответ: $\frac{4}{9}x^{16}y^{-18}$</p><p><strong>в)</strong> $(0.25a^{-3}b^4)^{-2} \cdot (2a^5b^{-6})^{-1}$</p><p>Представим $0.25$ как $\frac{1}{4}$ и применим свойства степеней:</p><p>$(0.25a^{-3}b^4)^{-2} = (\frac{1}{4})^{-2}(a^{-3})^{-2}(b^4)^{-2} = 4^2 a^{6} b^{-8} = 16a^6b^{-8}$</p><p>$(2a^5b^{-6})^{-1} = 2^{-1}(a^5)^{-1}(b^{-6})^{-1} = \frac{1}{2}a^{-5}b^6$</p><p>Перемножим результаты:</p><p>$(16a^6b^{-8}) \cdot (\frac{1}{2}a^{-5}b^6) = (16 \cdot \frac{1}{2}) \cdot (a^6a^{-5}) \cdot (b^{-8}b^6)$</p><p>Упростим, выполнив умножение коэффициентов и сложение показателей степеней:</p><p>$8 \cdot a^{6-5} \cdot b^{-8+6} = 8a^1b^{-2} = 8ab^{-2}$</p><p>Ответ: $8ab^{-2}$</p><p><strong>г)</strong> $(\frac{0.1a^{-2}}{b^{-1}c^3})^5 \cdot (\frac{b^5}{10a^4c^6})^{-3}$</p><p>Применим свойство $(\frac{a}{b})^{-n} = (\frac{b}{a})^n$ ко второму множителю. Заметим, что $0.1 = \frac{1}{10} = 10^{-1}$.</p><p>$(\frac{10^{-1}a^{-2}}{b^{-1}c^3})^5 \cdot (\frac{10a^4c^6}{b^5})^3$</p><p>Возведем каждую дробь в соответствующую степень:</p><p>$\frac{(10^{-1})^5(a^{-2})^5}{(b^{-1})^5(c^3)^5} \cdot \frac{10^3(a^4)^3(c^6)^3}{(b^5)^3} = \frac{10^{-5}a^{-10}}{b^{-5}c^{15}} \cdot \frac{10^3a^{12}c^{18}}{b^{15}}$</p><p>Перемножим дроби, сгруппировав подобные члены:</p><p>$\frac{(10^{-5} \cdot 10^3) \cdot (a^{-10}a^{12}) \cdot c^{18}}{(b^{-5}b^{15}) \cdot c^{15}} = \frac{10^{-2} \cdot a^{-10+12} \cdot c^{18}}{b^{-5+15} \cdot c^{15}} = \frac{10^{-2}a^2c^{18}}{b^{10}c^{15}}$</p><p>Применим свойство $\frac{a^m}{a^n} = a^{m-n}$ для переменной $c$:</p><p>$\frac{10^{-2}a^2c^{18-15}}{b^{10}} = \frac{10^{-2}a^2c^3}{b^{10}} = \frac{a^2c^3}{100b^{10}}$</p><p>Ответ: $\frac{a^2c^3}{100b^{10}}$</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "171904" "type" => "task" ] "previous" => array:2 [ "refs" => "171902" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1393 #items: array:1 [ 0 => App\Models\Book {#1303 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 10 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1290 #items: array:1 [ 0 => App\Models\Term {#1291 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1302 #items: array:1 [ 0 => App\Models\Term {#1301 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1300 #items: array:1 [ 0 => App\Models\Term {#1299 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:4 [ 0 => App\Models\Term {#1296 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1298 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1294 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 3 => App\Models\Term {#1292 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1295 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1293 #items: array:1 [ 0 => App\Models\Term {#1368 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1369 #items: array:1 [ 0 => App\Models\Term {#1371 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1372 #items: array:1 [ 0 => App\Models\Term {#1373 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1374 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1375 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1376 #items: array:1 [ 0 => App\Models\Term {#1377 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1378 #items: array:1 [ 0 => App\Models\Term {#1379 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publication_number" => "16" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1380 #items: array:1 [ 0 => App\Models\Term {#1381 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1382 #items: array:1 [ 0 => App\Models\Term {#1383 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "934" "field_priority" => "2" "field_default_folder" => "/algebra_09/makarychev-2023/" "field_isbn" => "978-5-09-112135-3" "field_cover" => array:1 [ 0 => "/media/algebra_09/makarychev-2023/covers/cover1.webp?ts=1734038732" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/makarychev-2023/covers/cover1.webp?ts=1734038732" "alt" => "" "width" => "680" "height" => "1065" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1384 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1385 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1386 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/makarychev-fgos" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1387 #items: array:3 [ 0 => App\Models\Term {#1388 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1389 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1390 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => "<!--Текст в низу страницы--> <h2> Учебный процесс с решебником Ключниковой </h2> <p> Изучение алгебры всегда связано с различными недопониманиями. Довольно часто у ребят не хватает времени, чтобы детально проработать каждый параграф. Теорию они проходят в спешке, так как основное внимание сосредоточено в основном на практических заданиях, которые учителя задают на дом в больших количествах. ГДЗ «<strong>Алгебра Учебник Макарычев, Миндюк, Нешков 9 класс (Просвещение, 2023г.)</strong>» позволит школьникам сбалансировать учебный процесс, не упуская ни одной мелочи. </p> <p> Многие ученики испытывают проблемы с пониманием таких аспектов: </p> <ol> <li>Действия над действительными числами.</li> <li>Погрешность и точность приближения?</li> <li>Свойства чётности и нечётности функций.</li> <li>Целое уравнение и его корни.</li> <li>Решение неравенств методом интервалов.</li> <li>Уравнение с двумя переменными и его график.</li> </ol> <p> Современные учебники часто снабжены недостаточно развернутой теорией, что мешает учащимся еще раз пробежаться по материалу, если они пропустили урок или не поняли объяснения преподавателя. Поэтому иногда подростки приступают к решению задач так до конца и не разобравшись в параграфах. Неудивительно, что потом в их работах обнаруживается много ошибок. Благодаря решебнику можно избежать любых недочетов при выполнении номеров. </p> <h2> Почему работать с решебником нужно правильно? </h2> <p> Школьники всегда делятся на две категории. Первые, даже с большим скрипом, но находят решения и ответы самостоятельно, а вот вторые постоянно списывают домашние задания и ничего толком в дисциплине не понимают. Но используя <strong>решебник по алгебре за 9 класс к учебнику Макарычева Ю.Н., Миндюка Н.Г., Нешкова К.И. 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Поэтому школьникам не только стоит быть предельно внимательными, но и систематически проверять себя по <strong>готовым решениям к учебнику Макарычева за 9 класс</strong>, написанными в соответствии с ФГОС. Сделать это очень просто, так как пособие находится в онлайн-доступе, и открыть его можно с любого гаджета, подключенного к Интернету. Тренировки со справочником не отнимают много времени, так как авторы снабдили его подробными решениями, верными ответами и многочисленными наглядными примерами, которые легко понять и запомнить. </p> <p> Онлайн-издание пригодится учащимся для многого: </p> <ul> <li>сверки д/з;</li> <li>подготовки к тестированиям;</li> <li>разбора проблематичных параграфов;</li> <li>проработки различных упущений, и т.д.</li> </ul> <p> Некоторые учителя сами советуют своим подопечным использовать решебник, так как прекрасно понимают, что иначе дети просто не справятся с программой. Конечно, есть и еще один вариант - занятия с репетитором. 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№714 (с. 193)
Условие. №714 (с. 193)
скриншот условия
714. Упростите выражение:
Решение 1. №714 (с. 193)
Решение 2. №714 (с. 193)
Решение 3. №714 (с. 193)
Решение 4. №714 (с. 193)
Решение 5. №714 (с. 193)
Решение 7. №714 (с. 193)
Решение 8. №714 (с. 193)
а) $(4x^{-2}y^3)^2 \cdot (0.5x^2y^{-1})^3$
Чтобы упростить выражение, сначала возведем каждый множитель в соответствующую степень, используя правила $(ab)^n = a^n b^n$ и $(a^m)^n = a^{mn}$:
$(4x^{-2}y^3)^2 = 4^2 \cdot (x^{-2})^2 \cdot (y^3)^2 = 16x^{-4}y^6$
$(0.5x^2y^{-1})^3 = (0.5)^3 \cdot (x^2)^3 \cdot (y^{-1})^3 = 0.125x^6y^{-3}$
Теперь перемножим полученные выражения, группируя коэффициенты и переменные с одинаковыми основаниями:
$(16x^{-4}y^6) \cdot (0.125x^6y^{-3}) = (16 \cdot 0.125) \cdot (x^{-4}x^6) \cdot (y^6y^{-3})$
Используя правило $a^m \cdot a^n = a^{m+n}$, завершим упрощение:
$2 \cdot x^{-4+6} \cdot y^{6+(-3)} = 2x^2y^3$
Ответ: $2x^2y^3$
б) $(\frac{c^4}{6x^2y^{-5}})^{-2} \cdot (\frac{1}{3}c^2x^3y^{-2})^4$
Для первого множителя применим свойство $(\frac{a}{b})^{-n} = (\frac{b}{a})^n$. Для второго — свойство $(abc)^n = a^n b^n c^n$.
$(\frac{c^4}{6x^2y^{-5}})^{-2} = (\frac{6x^2y^{-5}}{c^4})^2 = \frac{6^2(x^2)^2(y^{-5})^2}{(c^4)^2} = \frac{36x^4y^{-10}}{c^8}$
$(\frac{1}{3}c^2x^3y^{-2})^4 = (\frac{1}{3})^4(c^2)^4(x^3)^4(y^{-2})^4 = \frac{1}{81}c^8x^{12}y^{-8}$
Теперь перемножим полученные выражения:
$\frac{36x^4y^{-10}}{c^8} \cdot \frac{1}{81}c^8x^{12}y^{-8} = \frac{36}{81} \cdot \frac{c^8}{c^8} \cdot (x^4x^{12}) \cdot (y^{-10}y^{-8})$
Сократим дробь $\frac{36}{81}$ на 9 и сложим показатели степеней:
$\frac{4}{9} \cdot 1 \cdot x^{4+12} \cdot y^{-10-8} = \frac{4}{9}x^{16}y^{-18}$
Ответ: $\frac{4}{9}x^{16}y^{-18}$
в) $(0.25a^{-3}b^4)^{-2} \cdot (2a^5b^{-6})^{-1}$
Представим $0.25$ как $\frac{1}{4}$ и применим свойства степеней:
$(0.25a^{-3}b^4)^{-2} = (\frac{1}{4})^{-2}(a^{-3})^{-2}(b^4)^{-2} = 4^2 a^{6} b^{-8} = 16a^6b^{-8}$
$(2a^5b^{-6})^{-1} = 2^{-1}(a^5)^{-1}(b^{-6})^{-1} = \frac{1}{2}a^{-5}b^6$
Перемножим результаты:
$(16a^6b^{-8}) \cdot (\frac{1}{2}a^{-5}b^6) = (16 \cdot \frac{1}{2}) \cdot (a^6a^{-5}) \cdot (b^{-8}b^6)$
Упростим, выполнив умножение коэффициентов и сложение показателей степеней:
$8 \cdot a^{6-5} \cdot b^{-8+6} = 8a^1b^{-2} = 8ab^{-2}$
Ответ: $8ab^{-2}$
г) $(\frac{0.1a^{-2}}{b^{-1}c^3})^5 \cdot (\frac{b^5}{10a^4c^6})^{-3}$
Применим свойство $(\frac{a}{b})^{-n} = (\frac{b}{a})^n$ ко второму множителю. Заметим, что $0.1 = \frac{1}{10} = 10^{-1}$.
$(\frac{10^{-1}a^{-2}}{b^{-1}c^3})^5 \cdot (\frac{10a^4c^6}{b^5})^3$
Возведем каждую дробь в соответствующую степень:
$\frac{(10^{-1})^5(a^{-2})^5}{(b^{-1})^5(c^3)^5} \cdot \frac{10^3(a^4)^3(c^6)^3}{(b^5)^3} = \frac{10^{-5}a^{-10}}{b^{-5}c^{15}} \cdot \frac{10^3a^{12}c^{18}}{b^{15}}$
Перемножим дроби, сгруппировав подобные члены:
$\frac{(10^{-5} \cdot 10^3) \cdot (a^{-10}a^{12}) \cdot c^{18}}{(b^{-5}b^{15}) \cdot c^{15}} = \frac{10^{-2} \cdot a^{-10+12} \cdot c^{18}}{b^{-5+15} \cdot c^{15}} = \frac{10^{-2}a^2c^{18}}{b^{10}c^{15}}$
Применим свойство $\frac{a^m}{a^n} = a^{m-n}$ для переменной $c$:
$\frac{10^{-2}a^2c^{18-15}}{b^{10}} = \frac{10^{-2}a^2c^3}{b^{10}} = \frac{a^2c^3}{100b^{10}}$
Ответ: $\frac{a^2c^3}{100b^{10}}$
Другие задания:
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