Simplify ((x^2y^-2)^-1)^-1

${({(x^{2} y^{- 2})}^{- 1})}^{- 1}$

Step 1

Multiply the exponents in ${({(x^{2} y^{- 2})}^{- 1})}^{- 1}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x^{2} y^{- 2})}^{- - 1}$

Multiply $- 1$ by $- 1$ .

${(x^{2} y^{- 2})}^{1}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(x^{2} \frac{1}{y^{2}})}^{1}$

Step 3

Combine $x^{2}$ and $\frac{1}{y^{2}}$ .

${(\frac{x^{2}}{y^{2}})}^{1}$

Step 4

Simplify.

$\frac{x^{2}}{y^{2}}$