Answer
$\frac{256m^{8}}{t^{4}p^{8}}$
Work Step by Step
$(\frac{-4m^{2}}{tp^{2}})^{4}$ = $\frac{(-4m^{2})^{4}}{(tp^{2})^{4}}$ = $\frac{(-4)^{4}(m^{2})^{4}}{t^{4}(p^{2})^{4}}$ = $\frac{(-4)^{4}m^{2*4}}{t^{4}p^{2*4}}$ = $\frac{256m^{8}}{t^{4}p^{8}}$