Решебник по алгебре 8 класс Макарычев ФГОС Задание 117

\[\boxed{\text{117\ (117).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[\textbf{а)}\ \left( \frac{5a^{3}}{3b^{2}} \right)^{4} = \frac{\left( 5a^{3} \right)^{4}}{\left( 3b^{2} \right)^{4}} = \frac{625a^{12}}{81b^{8}}\]

\[\textbf{б)}\ \left( \frac{2x^{2}}{3y^{3}} \right)^{5}\ = \frac{\left( 2x^{2} \right)^{5}}{\left( 3y^{3} \right)^{5}} = \frac{32x^{10}}{243y^{15}}\]

\[\textbf{в)}\ \left( - \frac{10m^{2}}{n^{2}p} \right)^{3} = - \frac{\left( 10m^{2} \right)^{3}}{\left( n^{2}p \right)^{3}} =\]

\[= - \frac{1000m^{6}}{n^{6}p^{3}}\]

\[\textbf{г)}\ \left( - \frac{b^{3}c^{2}}{8a^{3}} \right)^{2} = \frac{\left( b^{3}c^{2} \right)^{2}}{\left( 8a^{3} \right)^{2}} = \frac{b^{6}c^{4}}{64a^{6}}\]

\[\boxed{\text{117.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

Пояснение.

Решение.

\[\textbf{а)}\ \left( \frac{x}{2y} \right)^{3} = \frac{x^{3}}{(2y)^{3}} = \frac{x^{3}}{8y^{3}}\]

\[\textbf{б)}\ \left( \frac{3a}{c} \right)^{4} = \frac{(3a)^{4}}{c^{4}} = \frac{81a^{4}}{c^{4}}\]

\[\textbf{в)}\ \left( \frac{n^{2}}{10m} \right)^{3} = \frac{\left( n^{2} \right)^{3}}{(10m)^{3}} =\]

\[= \frac{n^{6}}{1000m³}\]

\[\textbf{г)}\ \left( \frac{9a^{3}}{2b^{2}} \right)^{2} = \frac{\left( 9a^{3} \right)^{2}}{\left( 2b^{2} \right)^{2}} = \frac{81a^{6}}{4b^{4}}\]