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

The solution to [(x^{-2})^3]^{-1} is x^6

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simplify [(x^{-2})^3]^{-1}

simplify

[(x^{- 2})^{3}]^{- 1}

x^{6}

Solution steps

[(x^{- 2})^{3}]^{- 1}

(x^{- 2})^{3} : x^{- 6}

= [x^{- 6}]^{- 1}

Apply exponent rule:

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

= \frac{1}{x ^{- 6}}

Apply exponent rule:

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

x^{- 6} = \frac{1}{x ^{6}}

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

Apply the fraction rule:

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

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

Apply the fraction rule:

\frac{a}{1} = a

= x^{6}

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