\[\boxed{\text{117\ (117).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ \left( \frac{5a^{3}}{3b^{2}} \right)^{4} = \frac{\left( 5a^{3} \right)^{4}}{\left( 3b^{2} \right)^{4}} = \frac{625a^{12}}{81b^{8}}\]
\[\textbf{б)}\ \left( \frac{2x^{2}}{3y^{3}} \right)^{5}\ = \frac{\left( 2x^{2} \right)^{5}}{\left( 3y^{3} \right)^{5}} = \frac{32x^{10}}{243y^{15}}\]
\[\textbf{в)}\ \left( - \frac{10m^{2}}{n^{2}p} \right)^{3} = - \frac{\left( 10m^{2} \right)^{3}}{\left( n^{2}p \right)^{3}} =\]
\[= - \frac{1000m^{6}}{n^{6}p^{3}}\]
\[\textbf{г)}\ \left( - \frac{b^{3}c^{2}}{8a^{3}} \right)^{2} = \frac{\left( b^{3}c^{2} \right)^{2}}{\left( 8a^{3} \right)^{2}} = \frac{b^{6}c^{4}}{64a^{6}}\]