Simplify ((-3^2b^-2)/(a^8c^-4))^-1

${(\frac{- 3^{2} b^{- 2}}{a^{8} c^{- 4}})}^{- 1}$

Simplify.

Move $b^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{- 3^{2}}{a^{8} c^{- 4} b^{2}})}^{- 1}$

Move $c^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{- 3^{2} c^{4}}{a^{8} b^{2}})}^{- 1}$

Simplify the numerator.

Raise $3$ to the power of $2$ .

${(\frac{- 1 \cdot 9 c^{4}}{a^{8} b^{2}})}^{- 1}$

Multiply $- 1$ by $9$ .

${(\frac{- 9 c^{4}}{a^{8} b^{2}})}^{- 1}$

Move the negative in front of the fraction.

${(- \frac{(9) c^{4}}{a^{8} b^{2}})}^{- 1}$

Change the sign of the exponent by rewriting the base as its reciprocal.

$- \frac{a^{8} b^{2}}{9 c^{4}}$