Решебник по алгебре 8 класс Макарычев ФГОС Задание 136

\[\boxed{\text{136\ (136).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \frac{11m^{4}}{6n^{2}} \cdot \frac{5m}{6n^{3}}\ :\frac{11n^{3}}{12m^{3}} =\]

\[= \frac{11m^{4}}{6n^{2}} \cdot \frac{5m}{6n^{3}} \cdot \frac{12m^{3}}{11n^{3}} = \frac{5m^{8}}{3n^{8}}\]

\[\textbf{б)}\ \frac{8x^{3}}{7y^{3}}\ :\frac{4x^{4}}{49y^{2}}\ :\frac{7x}{y^{2}} =\]

\[= \frac{8x^{3}}{7y^{3}} \cdot \frac{49y^{2}}{4x^{4}} \cdot \frac{y^{2}}{7x} = \frac{2y}{x^{2}}\]

\[\boxed{\text{136.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

Пояснение.

Решение.

\[\textbf{а)}\ \frac{6x^{2}}{m^{3}n}\ :\frac{x}{3mn^{2}} = \frac{6x^{2}}{m^{3}n} \cdot \frac{3mn^{2}}{x} =\]

\[= \frac{6x \cdot x \cdot 3n \cdot mn}{m^{2} \cdot mn \cdot x} = \frac{18xn}{m^{2}}\]

\[\textbf{б)}\ \frac{35x^{2}y}{12ab}\ :\frac{7\text{xy}}{8ab^{2}} =\]

\[= \frac{35x^{2}y}{12ab} \cdot \frac{8ab^{2}}{7xy} =\]

\[= \frac{7xy \cdot 5x \cdot 2b \cdot 4ab}{3 \cdot 4ab \cdot 7xy} = \frac{10xb}{3}\]

\[\textbf{в)}\ \frac{8mx^{2}}{3y^{3}}\ :\left( 4m^{2}x \right) =\]

\[= \frac{8mx^{2}}{3y^{3}} \cdot \frac{1}{4m^{2}x} =\]

\[= \frac{2x \cdot 4mx}{3y^{3} \cdot m \cdot 4mx} = \frac{2x}{3my^{3}}\]

\[\textbf{г)}\ 15a^{2}bx\ :\frac{a^{3}b^{2}}{30x^{2}} =\]

\[= \frac{15a^{2}\text{bx}}{1} \cdot \frac{30x^{2}}{a^{3}b^{2}} =\]

\[= \frac{a^{2}b \cdot 15x \cdot 30x^{2}}{a^{2}b \cdot ab} = \frac{450x^{3}}{\text{ab}}\]