簡約 (\sqrt[13]{3x^2y})^{11}

解

簡約

(13 3 x^{2} y)^{11}

3^{\frac{11}{13}} (x^{2} y)^{\frac{11}{13}}

解答ステップ

(13 3 x^{2} y)^{11}

累乗根の規則を適用する:

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

= ((3 x^{2} y)^{\frac{1}{13}})^{11}

指数の規則を適用する:

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

= (3 x^{2} y)^{\frac{1}{13} \cdot 11}

\frac{1}{13} \cdot 11 = \frac{11}{13}

= (3 x^{2} y)^{\frac{11}{13}}

指数の規則を適用する:

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

= 3^{\frac{11}{13}} (x^{2} y)^{\frac{11}{13}}