Решебник по алгебре 8 класс Макарычев ФГОС Задание 115

 

\[\boxed{\text{115\ (115).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

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

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

\[\textbf{в)}\ \left( \frac{n^{2}}{10m} \right)^{3} = \frac{\left( n^{2} \right)^{3}}{(10m)^{3}} = \frac{n^{6}}{1000m^{3}}\]

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

\[\boxed{\text{115.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

Пояснение.

Решение.

\[\textbf{а)} - \frac{10x^{2}y^{2}}{9a^{2}} \cdot \frac{27a^{3}}{5xy} =\]

\[= - \frac{10x^{2}y^{2} \cdot 27a^{3}}{9a^{2} \cdot 5xy} =\]

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

\[= - 6xya\ \]

\[\textbf{б)}\ \frac{2m^{3}}{35a^{3}b^{2}} \cdot \left( - \frac{7a^{2}b}{6m} \right) =\]

\[= - \frac{2m^{3} \cdot 7a^{2}b}{35a^{3}b^{2} \cdot 6m} =\]

\[= - \frac{2 \cdot m^{3} \cdot 7 \cdot a^{2} \cdot b}{7 \cdot 5 \cdot a^{3} \cdot b^{2} \cdot 2 \cdot 3m} =\]

\[= - \frac{m²}{15ab}\]

\[\textbf{в)}\ \frac{13x}{12mn^{2}} \cdot 4m^{2}n =\]

\[= \frac{13x \cdot 4m^{2}n}{12mn^{2}} = \frac{13xm}{3n}\]

\[\textbf{г)} - ab \cdot \left( - \frac{11x^{2}}{3a^{2}b^{2}} \right) =\]

\[= \frac{ab \cdot 11x^{2}}{3a^{2}b^{2}} = \frac{a \cdot b \cdot 11 \cdot x^{2}}{3 \cdot a^{2} \cdot b^{2}} =\]

\[= \frac{11x^{2}}{3ab}\ \]