What is (-36)^{-1/2} ?

The solution to (-36)^{-1/2} is -1/6 i

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simplify (-36)^{-1/2}

simplify

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

- \frac{1}{6} i

Solution steps

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

Apply exponent rule:

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

(- 36)^{- \frac{1}{2}} = \frac{1}{( - 36 ) ^{\frac{1}{2}}}

= \frac{1}{( - 36 ) ^{\frac{1}{2}}}

(- 36)^{\frac{1}{2}} = 3 6^{\frac{1}{2}} i

= \frac{1}{3 6 ^{\frac{1}{2}} i}

3 6^{\frac{1}{2}} = 6

= \frac{1}{6 i}

Multiply by the conjugate

\frac{- i}{- i}

= \frac{1 \cdot ( - i )}{6 i ( - i )}

Simplify

\frac{1 \cdot ( - i )}{6 i ( - i )} : \frac{- i}{6}

= \frac{- i}{6}

Rewrite in standard complex form:

- \frac{1}{6} i

= - \frac{1}{6} i

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