簡約 (81x^{24}y^{-20})^{1/4}

解

簡約

(81 x^{24} y^{- 20})^{\frac{1}{4}}

\frac{3 x ^{6}}{y ^{5}}

解答ステップ

(81 x^{24} y^{- 20})^{\frac{1}{4}}

指数の規則を適用する:

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

(81 x^{24} y^{- 20})^{\frac{1}{4}} = 8 1^{\frac{1}{4}} (x^{24})^{\frac{1}{4}} (y^{- 20})^{\frac{1}{4}}

= 8 1^{\frac{1}{4}} (x^{24})^{\frac{1}{4}} (y^{- 20})^{\frac{1}{4}}

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

= 3 (x^{24})^{\frac{1}{4}} (y^{- 20})^{\frac{1}{4}}

簡素化

(x^{24})^{\frac{1}{4}} : x^{6}

= 3 x^{6} (y^{- 20})^{\frac{1}{4}}

簡素化

(y^{- 20})^{\frac{1}{4}} : \frac{1}{y ^{5}}

= 3 x^{6} \frac{1}{y ^{5}}

簡素化

3 x^{6} \frac{1}{y ^{5}} : \frac{3 x ^{6}}{y ^{5}}

= \frac{3 x ^{6}}{y ^{5}}