(A^1/4 *A^1/3)^12 при А=(3/4)^2/7 завтра контрольная, помогите пожалуйста

А=(3/4)^2/7

(A^1/4 *A^1/3)^12 = (A^1/2)^12 = A^6

Подставляем значение А:

A^6 = ((3/4)^2/7)^6 = (3/4)^(12/7) = (3/4)^(1.714)

Ответ: (3/4)^(1.714)

Давайте разберём выражение ((A^{1/4} \cdot A^{1/3})^{12}) шаг за шагом, подставив значение (A = \left(\frac{3}{4}\right)^{2/7}).

1. Преобразуем внутреннюю часть выражения:

   У нас есть произведение степеней с одинаковым основанием (A), то есть (A^{1/4} \cdot A^{1/3}).

   Воспользуемся свойством степеней: (A^m \cdot A^n = A^{m+n}).

   Таким образом, (A^{1/4} \cdot A^{1/3} = A^{1/4 + 1/3}).

2. Сложим показатели степеней:

   Чтобы сложить дроби (\frac{1}{4}) и (\frac{1}{3}), приведём их к общему знаменателю.

   Общий знаменатель для 4 и 3 — это 12.

   [ \frac{1}{4} = \frac{3}{12}, \quad \frac{1}{3} = \frac{4}{12} ]

   [ \frac{1}{4} + \frac{1}{3} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12} ]

   Таким образом, (A^{1/4} \cdot A^{1/3} = A^{7/12}).

3. Возведём в степень 12:

   Теперь у нас есть выражение ((A^{7/12})^{12}).

   Воспользуемся свойством степеней: ((A^m)^n = A^{m \cdot n}).

   [ (A^{7/12})^{12} = A^{(7/12) \cdot 12} = A^{7} ]

4. Подставим значение (A):

   Мы знаем, что (A = \left(\frac{3}{4}\right)^{2/7}).

   Тогда (A^7 = \left(\left(\frac{3}{4}\right)^{2/7}\right)^7).

   Используем свойство степеней снова: ((B^m)^n = B^{m \cdot n}).

   [ \left(\left(\frac{3}{4}\right)^{2/7}\right)^7 = \left(\frac{3}{4}\right)^{2/7 \cdot 7} = \left(\frac{3}{4}\right)^2 ]

5. Возведём в квадрат:

   [ \left(\frac{3}{4}\right)^2 = \frac{3^2}{4^2} = \frac{9}{16} ]

Таким образом, значение выражения ((A^{1/4} \cdot A^{1/3})^{12}) при (A = \left(\frac{3}{4}\right)^{2/7}) равно (\frac{9}{16}).

Для того чтобы решить данное выражение, сначала выразим А в виде дроби с общим знаменателем:

A = (3/4)^(2/7) = (3^2 / 4^2)^(1/7) = 9/16

Теперь подставим значение А в исходное выражение:

(A^(1/4) A^(1/3))^12 = ((9/16)^(1/4) (9/16)^(1/3))^12 = (3/4 * (3/4)^(1/3))^12

Далее упростим:

(3/4 (3/4)^(1/3))^12 = (3/4 (3^(1/3) / 4^(1/3)))^12 = (3/4 3^(1/3) / 4^(1/3))^12 = (3/4 3^(1/3) 4^(-1/3))^12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) 12 = 3/4 3^(1/3) 4^(-1/3) * 12 = 3/