簡約 (\sqrt[5]{2^2x^3})^4

解

簡約

(5 2^{2} x^{3})^{4}

4^{\frac{4}{5}} x^{\frac{12}{5}}

解答ステップ

(5 2^{2} x^{3})^{4}

累乗根の規則を適用する:

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

= ((2^{2} x^{3})^{\frac{1}{5}})^{4}

指数の規則を適用する:

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

= (2^{2} x^{3})^{\frac{1}{5} \cdot 4}

\frac{1}{5} \cdot 4 = \frac{4}{5}

= (2^{2} x^{3})^{\frac{4}{5}}

2^{2} = 4

= (4 x^{3})^{\frac{4}{5}}

指数の規則を適用する:

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

= 4^{\frac{4}{5}} (x^{3})^{\frac{4}{5}}

(x^{3})^{\frac{4}{5}} : x^{\frac{12}{5}}

= 4^{\frac{4}{5}} x^{\frac{12}{5}}