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Popular >

simplify (-9)^{-1/2}

Solution

simplify

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

Solution

- \frac{1}{3} i

Solution steps

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

Apply exponent rule:

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

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

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

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

= \frac{1}{9 ^{\frac{1}{2}} i}

9^{\frac{1}{2}} = 3

= \frac{1}{3 i}

Multiply by the conjugate

\frac{- i}{- i}

= \frac{1 \cdot ( - i )}{3 i ( - i )}

Simplify

\frac{1 \cdot ( - i )}{3 i ( - i )} : \frac{- i}{3}

= \frac{- i}{3}

Rewrite in standard complex form:

- \frac{1}{3} i

= - \frac{1}{3} i

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Frequently Asked Questions (FAQ)

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