簡約-(1/(-3sqrt(3)))^{1/3}

解

簡約

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

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

十進法表記

0.57735 \dots

解答ステップ

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

指数の規則を適用する:

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

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

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

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

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

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

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