簡約 (12x^3y^{-2})^{2/3}

解

簡約

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

\frac{1 2 ^{\frac{2}{3}} x ^{2}}{y ^{\frac{4}{3}}}

解答ステップ

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

指数の規則を適用する:

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

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

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

簡素化

(x^{3})^{\frac{2}{3}} : x^{2}

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

簡素化

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

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

簡素化

1 2^{\frac{2}{3}} x^{2} \frac{1}{y ^{\frac{4}{3}}} : \frac{1 2 ^{\frac{2}{3}} x ^{2}}{y ^{\frac{4}{3}}}

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