簡約 (125x^6)^{2/3}

解

簡約

(125 x^{6})^{\frac{2}{3}}

25 x^{4}

解答ステップ

(125 x^{6})^{\frac{2}{3}}

指数の規則を適用する:

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

(125 x^{6})^{\frac{2}{3}} = 12 5^{\frac{2}{3}} (x^{6})^{\frac{2}{3}}

= 12 5^{\frac{2}{3}} (x^{6})^{\frac{2}{3}}

12 5^{\frac{2}{3}} = 25

= 25 (x^{6})^{\frac{2}{3}}

指数の規則を適用する:

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

, 以下を想定

a \geq 0

(x^{6})^{\frac{2}{3}} = x^{6 \cdot \frac{2}{3}}

= 25 x^{6 \cdot \frac{2}{3}}

6 \cdot \frac{2}{3} = 4

= 25 x^{4}