Answer
$ \displaystyle \frac{1}{9x^{5}}$
Work Step by Step
$$\begin{align*}
\displaystyle \frac{3^{-2}\cdot x^{-5}}{y^{0}} &=\displaystyle \frac{\boxed{3^{-2}}\cdot\boxed{x^{-5}}}{y^{0}} \\
&\small\text{For any integer $n$ and any nonzero number $a$, the number $a^{-n}$ is the reciprocal of $a^{n}$.} \\
& =\displaystyle \frac{\frac{1}{3^{2}}\cdot\frac{1}{x^{5}}}{y^{0}} \\
&\small\text{For any nonzero number $a$, the number $a^{0}=1$.} \\
& =\displaystyle \frac{\frac{1}{9}\cdot\frac{1}{x^{5}}}{1} \\
&=\displaystyle \frac{1}{9}\cdot\frac{1}{x^{5}} \\
&= \displaystyle \frac{1}{9x^{5}} \end{align*}$$
