\[\boxed{\text{474\ (474).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ \left( 5x^{2}y^{3} \right)^{2} = 25 \cdot \left( x^{2} \right)^{2}\left( y^{3} \right)^{2} =\]
\[= 25x^{4}y^{6}\]
\[\textbf{б)}\ \left( - 4ax^{3} \right)^{3} =\]
\[= ( - 4)^{3} \cdot a^{3} \cdot \left( x^{3} \right)^{3} = - 64a^{3}x^{9}\]
\[\textbf{в)}\ \left( - 2m^{3}n^{2} \right)^{4} =\]
\[= ( - 2)^{4} \cdot \left( m^{3} \right)^{4}\left( n^{2} \right)^{4} =\]
\[= 16m^{12}n^{8}\]
\[\textbf{г)}\ \left( - a^{2}bc^{3} \right)^{5} = \left( - a^{2} \right)^{5}b^{5}\left( c^{3} \right)^{5} =\]
\[= - a^{10}b^{5}c^{15}\ \]