簡約 ((6/7)/(4/5))^3

解

簡約

(\frac{\frac{6}{7}}{\frac{4}{5}})^{3}

\frac{3375}{2744}

十進法表記

1.22995 \dots

解答ステップ

(\frac{\frac{6}{7}}{\frac{4}{5}})^{3}

指数の規則を適用する:

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

= \frac{( \frac{6}{7} ) ^{3}}{( \frac{4}{5} ) ^{3}}

(\frac{6}{7})^{3} = \frac{216}{343}

= \frac{\frac{216}{343}}{( \frac{4}{5} ) ^{3}}

(\frac{4}{5})^{3} = \frac{64}{125}

= \frac{\frac{216}{343}}{\frac{64}{125}}

\frac{\frac{216}{343}}{\frac{64}{125}} = \frac{3375}{2744}

= \frac{3375}{2744}