What is (-81)^{-3/2} ?

The solution to (-81)^{-3/2} is 1/729 i

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simplify (-81)^{-3/2}

simplify

(- 81)^{- \frac{3}{2}}

\frac{1}{729} i

Solution steps

(- 81)^{- \frac{3}{2}}

Apply exponent rule:

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

(- 81)^{- \frac{3}{2}} = \frac{1}{( - 81 ) ^{\frac{3}{2}}}

= \frac{1}{( - 81 ) ^{\frac{3}{2}}}

Simplify

\frac{1}{( - 81 ) ^{\frac{3}{2}}} : - \frac{1}{729 i}

= - \frac{1}{729 i}

Multiply by the conjugate

\frac{- i}{- i}

= - \frac{1 \cdot ( - i )}{729 i ( - i )}

Simplify

- \frac{1 \cdot ( - i )}{729 i ( - i )} : - \frac{- i}{729}

= - \frac{- i}{729}

Apply the fraction rule:

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

= \frac{i}{729}

Rewrite in standard complex form:

\frac{1}{729} i

= \frac{1}{729} i

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