簡約 [(5/2)^3]^{-4}*(4/5)^{-2}

解

簡約

[(\frac{5}{2})^{3}]^{- 4} \cdot (\frac{4}{5})^{- 2}

\frac{256}{9765625}

十進法表記

0.0000262144

解答ステップ

((\frac{5}{2})^{3})^{- 4} (\frac{4}{5})^{- 2}

((\frac{5}{2})^{3})^{- 4} = \frac{4096}{244140625}

= \frac{4096}{244140625} (\frac{4}{5})^{- 2}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

(\frac{4}{5})^{- 2} = \frac{1}{( \frac{4}{5} ) ^{2}}

= \frac{4096}{244140625} \cdot \frac{1}{( \frac{4}{5} ) ^{2}}

(\frac{4}{5})^{2} = \frac{16}{25}

= \frac{4096}{244140625} \cdot \frac{1}{\frac{16}{25}}

分数の規則を適用する:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{4096}{244140625} \cdot \frac{25}{16}

\frac{4096}{244140625} \cdot \frac{25}{16} = \frac{256}{9765625}

= \frac{256}{9765625}