簡約 ((-27}{64})^{\frac{-1)/3}

解

簡約

(\frac{- 27}{64})^{\frac{- 1}{3}}

- \frac{4}{3}

十進法表記

- 1.33333 \dots

解答ステップ

(\frac{- 27}{64})^{\frac{- 1}{3}}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( - 27 ) ^{\frac{- 1}{3}}}{6 4 ^{\frac{- 1}{3}}}

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

= \frac{- \frac{1}{3}}{6 4 ^{\frac{- 1}{3}}}

6 4^{\frac{- 1}{3}} = \frac{1}{4}

= \frac{- \frac{1}{3}}{\frac{1}{4}}

\frac{- \frac{1}{3}}{\frac{1}{4}} = - \frac{4}{3}

= - \frac{4}{3}