What is (1/(2a^{-2)})^{-3} ?

The solution to (1/(2a^{-2)})^{-3} is 8/(a^6)

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simplify (1/(2a^{-2)})^{-3}

simplify

(\frac{1}{2 a ^{- 2}})^{- 3}

\frac{8}{a ^{6}}

Solution steps

(\frac{1}{2 a ^{- 2}})^{- 3}

Apply exponent rule:

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

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

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

Simplify

(\frac{1}{2 a ^{- 2}})^{3} : \frac{a ^{6}}{8}

= \frac{1}{\frac{a ^{6}}{8}}

Apply the fraction rule:

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

= \frac{8}{a ^{6}}

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