Answer
$\frac{64a^{24}}{b^{30}}$
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, $(\frac{-2a^{4}}{b^{5}})^{6}=(\frac{-1\times2\times a^{4}}{b^{5}})^{6}=\frac{(-1)^{1\times6}2^{1\times6}a^{4\times6}}{b^{5\times6}}=\frac{(-1)^{6}\times2^{6}\times a^{24}}{b^{30}}=\frac{1\times64\times a^{24}}{b^{30}}=\frac{64a^{24}}{b^{30}}$.
