Решебник по алгебре 8 класс Макарычев ФГОС Задание 135

 

\[\boxed{\text{135\ (135).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \frac{3x^{2}}{5y^{3}}\ :\frac{9x^{3}}{2y^{2}} \cdot \frac{5y}{3x} =\]

\[= \frac{3x^{2}}{5y^{3}} \cdot \frac{2y^{2}}{9x^{3}} \cdot \frac{5y}{3x} =\]

\[= \frac{3x^{2} \cdot 2y^{2} \cdot 5y}{5y^{3} \cdot 9x^{3} \cdot 3x} = \frac{2}{9x^{2}}\]

\[\textbf{б)}\ \frac{7p^{4}}{10q^{3}} \cdot \frac{5q}{14p^{2}}\ :\frac{3p}{4q^{4}} =\]

\[= \frac{7p^{4}}{10q^{3}} \cdot \frac{5q}{14p^{2}} \cdot \frac{4q^{4}}{3p} =\]

\[= \frac{7p^{4} \cdot 5q \cdot 4q^{4}}{10q^{3} \cdot 14p^{2} \cdot 3p} = \frac{pq^{2}}{3}\]

\[\boxed{\text{135.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

Пояснение.

Решение.

\[\textbf{а)}\ \frac{6x^{2}}{5y}\ :\frac{3x}{10y^{3}} = \frac{6x^{2}}{5y} \cdot \frac{10y^{3}}{3x} =\]

\[= \frac{2x \cdot 3x \cdot 5y \cdot 2y^{2}}{5y \cdot 3x} = \frac{4xy^{2}}{1} =\]

\[= 4xy^{2}\]

\[\textbf{б)}\ \frac{8c}{21d^{2}}\ :\frac{6c^{2}}{7d} = \frac{8c}{21d^{2}} \cdot \frac{7d}{6c^{2}} =\]

\[= \frac{4 \cdot 2c \cdot 7d}{3d \cdot 7d \cdot 3c \cdot 2c} = \frac{4}{9cd}\]

\[\textbf{в)}\ \frac{3ab}{4xy}\ :\left( - \frac{21a^{2}b}{10x^{2}y} \right) =\]

\[= - \frac{3ab}{4xy} \cdot \frac{10x^{2}y}{21a^{2}b} =\]

\[= - \frac{3ab \cdot 2xy \cdot 5x}{2 \cdot 2xy \cdot 3ab \cdot 7a} = - \frac{5x}{14a}\]

\[\textbf{г)} - \frac{18a^{2}b^{2}}{5cd}\ :\left( - \frac{9ab^{3}}{5c^{2}d^{4}} \right) =\]

\[= \frac{18a^{2}b^{2}}{5cd} \cdot \frac{5c^{2}d^{4}}{9ab^{3}} =\]

\[= \frac{2a \cdot 9ab^{2} \cdot 5cd \cdot cd^{3}}{5cd \cdot 9ab^{2} \cdot b} = \frac{2acd^{3}}{b}\]