Решебник по алгебре 8 класс Макарычев ФГОС Задание 116

\[\boxed{\text{116\ (116).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[\textbf{а)}\ \left( \frac{2a}{p^{2}q^{3}} \right)^{4} = \frac{(2a)^{4}}{\left( p^{2}q^{3} \right)^{4}} = \frac{16a^{4}}{p^{8}q^{12}}\ \]

\[\textbf{б)}\ \left( \frac{3a^{2}b^{3}}{s^{4}} \right)^{2} = \frac{\left( 3a^{2}b^{3} \right)^{2}}{\left( s^{4} \right)^{2}} =\]

\[= \frac{9a^{4}b^{6}}{s^{8}}\]

\[\textbf{в)}\ \left( - \frac{2a^{2}b}{3mn^{3}} \right)^{2} = \frac{\left( 2a^{2}b \right)^{2}}{\left( 3mn^{3} \right)^{2}} =\]

\[= \frac{4a^{4}b^{2}}{9m^{2}n^{6}}\]

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

\[= - \frac{27x^{6}}{8y^{9}}\]

\[\boxed{\text{116.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

Пояснение.

Решение.

\[\textbf{а)}\ \frac{2a^{2}b}{3\text{xy}} \cdot \frac{3x^{2}y}{4ab^{2}} \cdot \frac{6\text{ax}}{15b^{2}} =\]

\[= \frac{2 \cdot a^{2}b \cdot 3 \cdot x^{2}y \cdot 3 \cdot 2\text{ax}}{3 \cdot \text{xy} \cdot 4ab^{2} \cdot 5 \cdot 3 \cdot b^{2}} =\]

\[= \frac{a²x²}{5b³}\ \]

\[\textbf{б)}\ \frac{6m^{3}n^{2}}{35p^{3}} \cdot \frac{49n^{4}}{m^{5}p^{3}} \cdot \frac{5m^{4}p^{2}}{42n^{6}} =\]

\[= \frac{{6 \cdot m}^{3}n^{2} \cdot 7 \cdot 7 \cdot n^{4} \cdot 5 \cdot m^{4}p^{2}}{5 \cdot 7 \cdot p^{3}{\cdot m}^{5}p^{3{\cdot 7 \cdot 6 \cdot n}^{6}}} =\]

\[= \frac{m^{2}}{p^{4}}\]