簡約 \sqrt[5]{4x^2}*\sqrt[5]{4x^2}

解

簡約

5 4 x^{2} \cdot 5 4 x^{2}

5 4^{2} 5 x^{4}

解答ステップ

5 4 x^{2} 5 4 x^{2}

累乗根の規則を適用する:

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

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

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

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

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

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

\frac{1}{5} + \frac{1}{5} = \frac{2}{5}

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

指数の規則を適用する:

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

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

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

簡素化

(x^{2})^{\frac{2}{5}} : x^{\frac{4}{5}}

= 4^{\frac{2}{5}} x^{\frac{4}{5}}

4^{\frac{2}{5}} = 5 4^{2}

= 5 4^{2} 5 x^{4}

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

= 5 4^{2} 5 x^{4}