What is (-4)^{-3/2} ?

The solution to (-4)^{-3/2} is 1/8 i

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simplify (-4)^{-3/2}

simplify

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

\frac{1}{8} i

Solution steps

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

Apply exponent rule:

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

(- 4)^{- \frac{3}{2}} = \frac{1}{( - 4 ) ^{\frac{3}{2}}}

= \frac{1}{( - 4 ) ^{\frac{3}{2}}}

Simplify

\frac{1}{( - 4 ) ^{\frac{3}{2}}} : - \frac{1}{8 i}

= - \frac{1}{8 i}

Multiply by the conjugate

\frac{- i}{- i}

= - \frac{1 \cdot ( - i )}{8 i ( - i )}

Simplify

- \frac{1 \cdot ( - i )}{8 i ( - i )} : - \frac{- i}{8}

= - \frac{- i}{8}

Apply the fraction rule:

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

= \frac{i}{8}

Rewrite in standard complex form:

\frac{1}{8} i

= \frac{1}{8} i

e^{t} (e^{- t})