Answer
$$\text{D}$$
Work Step by Step
RECALL:
(1) $(a^m)^n=a^{mn}$'
(2) $(ab)^m=a^mb^m$
(3) $a^{-m} = \dfrac{1}{a^m}, a \ne 0$
Use rule (2) above to obtain:
\begin{align*}
\left(-6y^{-4}\right)^5&=(-6)^5\left(y^{-4}\right)^5\\
&=-7776\left(y^{-4}\right)^5
\end{align*}
Use rule (1) above to obtain:
\begin{align*}
-7776\left(y^{-4}\right)^5&=-7776y^{-4\cdot 5}\\
&=-7776y^{-20}
\end{align*}
Use rule (3) above to obtain:
\begin{align*}
-7776y^{-20}&=-7776 \cdot \dfrac{1}{y^{20}}\\
&=-\dfrac{7776}{y^{20}}
\end{align*}
Thus, the answer is Option $\text{D}$.
