簡約 (4/9)^{(-3)/2}

解

簡約

(\frac{4}{9})^{\frac{- 3}{2}}

\frac{27}{8}

十進法表記

3.375

解答ステップ

(\frac{4}{9})^{\frac{- 3}{2}}

指数の規則を適用する:

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

= \frac{4 ^{\frac{- 3}{2}}}{9 ^{\frac{- 3}{2}}}

4^{\frac{- 3}{2}} = \frac{1}{8}

= \frac{\frac{1}{8}}{9 ^{\frac{- 3}{2}}}

9^{\frac{- 3}{2}} = \frac{1}{27}

= \frac{\frac{1}{8}}{\frac{1}{27}}

\frac{\frac{1}{8}}{\frac{1}{27}} = \frac{27}{8}

= \frac{27}{8}