簡約 (-27/64)^{4/3}

解

簡約

(- \frac{27}{64})^{\frac{4}{3}}

\frac{81}{256}

十進法表記

0.31640625

解答ステップ

(- \frac{27}{64})^{\frac{4}{3}}

指数の規則を適用する:

(- a)^{\frac{m}{n}} = (- 1)^{\frac{m}{n}} (a)^{\frac{m}{n}}

(- \frac{27}{64})^{\frac{4}{3}} = (- 1)^{\frac{4}{3}} (\frac{27}{64})^{\frac{4}{3}}

= (- 1)^{\frac{4}{3}} (\frac{27}{64})^{\frac{4}{3}}

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

= 1 \cdot (\frac{27}{64})^{\frac{4}{3}}

指数の規則を適用する:

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

(\frac{27}{64})^{\frac{4}{3}} = \frac{2 7 ^{\frac{4}{3}}}{6 4 ^{\frac{4}{3}}}

= 1 \cdot \frac{2 7 ^{\frac{4}{3}}}{6 4 ^{\frac{4}{3}}}

6 4^{\frac{4}{3}} = 256

= 1 \cdot \frac{2 7 ^{\frac{4}{3}}}{256}

2 7^{\frac{4}{3}} = 81

= 1 \cdot \frac{81}{256}

乗算:

1 \cdot \frac{81}{256} = \frac{81}{256}

= \frac{81}{256}