簡約 (2/3)^{2/3}*(3/2)^{-1/3}

解

簡約

(\frac{2}{3})^{\frac{2}{3}} \cdot (\frac{3}{2})^{- \frac{1}{3}}

\frac{2}{3}

十進法表記

0.66666 \dots

解答ステップ

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

(\frac{2}{3})^{\frac{2}{3}} = (\frac{4}{9})^{\frac{1}{3}}

= (\frac{4}{9})^{\frac{1}{3}} (\frac{3}{2})^{- \frac{1}{3}}

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

= (\frac{4}{9})^{\frac{1}{3}} (\frac{2}{3})^{\frac{1}{3}}

(\frac{4}{9})^{\frac{1}{3}} = (\frac{2}{3})^{\frac{2}{3}}

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

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

(\frac{2}{3})^{\frac{2}{3}} (\frac{2}{3})^{\frac{1}{3}} = (\frac{2}{3})^{\frac{2}{3} + \frac{1}{3}}

= (\frac{2}{3})^{\frac{2}{3} + \frac{1}{3}}

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

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

指数の規則を適用する:

a^{1} = a

= \frac{2}{3}