簡約 (x^{(-2)/3}*y^{(-1)/2})^2

解

簡約

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

\frac{1}{y x ^{\frac{4}{3}}}

解答ステップ

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

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

簡素化

(x^{\frac{- 2}{3}})^{2} : \frac{1}{x ^{\frac{4}{3}}}

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

簡素化

(y^{\frac{- 1}{2}})^{2} : \frac{1}{y}

= \frac{1}{x ^{\frac{4}{3}}} \cdot \frac{1}{y}

簡素化

\frac{1}{x ^{\frac{4}{3}}} \cdot \frac{1}{y} : \frac{1}{y x ^{\frac{4}{3}}}

= \frac{1}{y x ^{\frac{4}{3}}}