What is (-9)^{-3/2} ?

The solution to (-9)^{-3/2} is 1/27 i

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simplify (-9)^{-3/2}

simplify

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

\frac{1}{27} i

Solution steps

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

Apply exponent rule:

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

(- 9)^{- \frac{3}{2}} = \frac{1}{( - 9 ) ^{\frac{3}{2}}}

= \frac{1}{( - 9 ) ^{\frac{3}{2}}}

Simplify

\frac{1}{( - 9 ) ^{\frac{3}{2}}} : - \frac{1}{27 i}

= - \frac{1}{27 i}

Multiply by the conjugate

\frac{- i}{- i}

= - \frac{1 \cdot ( - i )}{27 i ( - i )}

Simplify

- \frac{1 \cdot ( - i )}{27 i ( - i )} : - \frac{- i}{27}

= - \frac{- i}{27}

Apply the fraction rule:

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

= \frac{i}{27}

Rewrite in standard complex form:

\frac{1}{27} i

= \frac{1}{27} i

9 - x^{2} \cdot x^{2} - 4

(z^{4} - 3 z^{3} + 2 z^{2} - 4 z + 4) (z - 1)^{- 1}

j^{2} (j + 1)^{2}

(x + 1)^{- 1}

(0.045 x^{750}) x^{4}