Решебник по алгебре 8 класс Макарычев ФГОС Задание 119

\[\boxed{\text{119\ (119).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[\textbf{а)}\ \frac{x^{2} - xy}{y} \cdot \frac{y^{2}}{x} =\]

\[= \frac{x \cdot (x - y) \cdot y^{2}}{y \cdot x} = y \cdot (x - y) =\]

\[= xy - y^{2}\]

\[\textbf{б)}\frac{3a}{b^{2}} \cdot \frac{ab + b^{2}}{9} =\]

\[= \frac{3a \cdot b \cdot (a + b)}{9b^{2}} = \frac{a(a + b)}{3b} =\]

\[= \frac{a^{2} + ab}{3b}\]

\[\boxed{\text{119.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

Пояснение.

Решение.

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

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

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

\[= - \frac{1000m^{6}}{n^{6}p³}\]

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