What is (x^2*y^{-3})^{-2} ?

The solution to (x^2*y^{-3})^{-2} is (y^6)/(x^4)

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simplify (x^2*y^{-3})^{-2}

simplify

(x^{2} \cdot y^{- 3})^{- 2}

\frac{y ^{6}}{x ^{4}}

Solution steps

(x^{2} y^{- 3})^{- 2}

Apply exponent rule:

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

(x^{2} y^{- 3})^{- 2} = \frac{1}{( x ^{2} y ^{- 3} ) ^{2}}

= \frac{1}{( x ^{2} y ^{- 3} ) ^{2}}

Simplify

(x^{2} y^{- 3})^{2} : \frac{x ^{4}}{y ^{6}}

= \frac{1}{\frac{x ^{4}}{y ^{6}}}

Apply the fraction rule:

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

= \frac{y ^{6}}{x ^{4}}

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