$$ (-5m^4n^2)^2 = (-5)^2 \cdot (m^4)^2 \cdot (n^2)^2 = 25m^{4 \cdot 2}n^{2 \cdot 2} = 25m^8n^4 $$.
Ответ: $$ 25m^8n^4 $$