\[\boxed{\text{271\ (271).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1) - 4m^{3}n^{5} \cdot 5m^{4}n^{2} =\]
\[= - 20m^{7}n^{7}\]
\[2)\ \left( - 2m^{7}n^{2} \right)^{4} = 16m^{28}n^{8}\]
\[3)\ 8x^{3}y^{4} \cdot \left( - \frac{1}{2}x^{2}y^{5} \right)^{3} =\]
\[= - 8x^{3}y^{4} \cdot \frac{1}{8}x^{6}y^{15} = - x^{9}y^{19}\]