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Popular >

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

Solution

simplify

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

Solution

i

Solution steps

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

Apply exponent rule:

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

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

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

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

= \frac{1}{i ^{3}}

i^{3} = - i

= \frac{1}{- i}

Apply the fraction rule:

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

= - \frac{1}{i}

Multiply by the conjugate

\frac{- i}{- i}

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

Simplify

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

= - \frac{- i}{1}

Simplify

- \frac{- i}{1} : i

= i

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Frequently Asked Questions (FAQ)

What is (-1)^{-3/2} ?
The solution to (-1)^{-3/2} is i