What is (x^2y^{-1})^{-3} ?

The solution to (x^2y^{-1})^{-3} is (y^3)/(x^6)

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simplify (x^2y^{-1})^{-3}

simplify

(x^{2} y^{- 1})^{- 3}

\frac{y ^{3}}{x ^{6}}

Solution steps

(x^{2} y^{- 1})^{- 3}

Apply exponent rule:

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

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

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

Simplify

(x^{2} y^{- 1})^{3} : \frac{x ^{6}}{y ^{3}}

= \frac{1}{\frac{x ^{6}}{y ^{3}}}

Apply the fraction rule:

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

= \frac{y ^{3}}{x ^{6}}

(3 x^{4} y^{2})^{4}

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