化简 (-36)^{-1/2}

解答

化简

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

- \frac{1}{6} i

求解步骤

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

使用指数法则:

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}

乘以共轭根式

\frac{- i}{- i}

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

化简

\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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