Answer
$\frac{k^5}{9}$
Work Step by Step
We rewrite the given expression as a division problem: $3^{-2}\div k^{-5}$
The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. We use this rule to rewrite the expression:
$\frac{1}{3^{2}}\div\frac{1}{k^5}$
To divide by a fraction, we multiply by the reciprocal: $\frac{1}{3^2}\times\frac{k^5}{1}$
To multiply fractions, we multiply the numerators and the denominators: $\frac{k^5}{3^2}$
We expand the exponent in the denominator: $\frac{k^5}{3^2}=\frac{k^5}{9}$
