Answer
$-\frac{64m^{6}}{t^{3}}$
Work Step by Step
According to the power rule for exponents, $(a^{m})^{n}=a^{mn}$ (where $m$ and $n$ are integers and $a$ is a real number).
Therefore, $(\frac{-4m^{2}}{t})^{3}=(\frac{-1\times4\times m^{2}}{t})^{3}=\frac{(-1)^{1\times3}4^{1\times3}m^{2\times3}}{t^{1\times3}}=\frac{(-1)^{3}4^{3}m^{6}}{t^{3}}=\frac{-1\times64\times m^{6}}{t^{3}}=\frac{-64m^{6}}{t^{3}}=-\frac{64m^{6}}{t^{3}}$.