Answer
$\frac{1}{a^{2}}$
Work Step by Step
We are given the expression $(\frac{a^{-4}}{a^{-5}})^{-2}$.
First, we can use the power rule to simplify.
$(\frac{a^{-4}}{a^{-5}})^{-2}=\frac{a^{-4\times-2}}{a^{-5\times-2}}=\frac{a^{8}}{a^{10}}$
Next, we can use the quotient rule.
$a^{8-10}=a^{-2}=\frac{1}{a^{2}}$
