簡約 (\sqrt[6]{5xy^5})^5

解

簡約

(6 5 x y^{5})^{5}

5^{\frac{5}{6}} (x y^{5})^{\frac{5}{6}}

解答ステップ

(6 5 x y^{5})^{5}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

= ((5 x y^{5})^{\frac{1}{6}})^{5}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (5 x y^{5})^{\frac{1}{6} \cdot 5}

\frac{1}{6} \cdot 5 = \frac{5}{6}

= (5 x y^{5})^{\frac{5}{6}}

指数の規則を適用する:

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

= 5^{\frac{5}{6}} (x y^{5})^{\frac{5}{6}}