What is (x^{-2}y^2)^{-2} ?

The solution to (x^{-2}y^2)^{-2} is (x^4)/(y^4)

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simplify (x^{-2}y^2)^{-2}

simplify

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

\frac{x ^{4}}{y ^{4}}

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(x^{- 2} y^{2})^{- 2} = \frac{1}{( x ^{- 2} y ^{2} ) ^{2}}

= \frac{1}{( x ^{- 2} y ^{2} ) ^{2}}

Simplify

(x^{- 2} y^{2})^{2} : \frac{y ^{4}}{x ^{4}}

= \frac{1}{\frac{y ^{4}}{x ^{4}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{x ^{4}}{y ^{4}}

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