簡約 (27x^6)^{2/3}

解

簡約

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

9 x^{4}

解答ステップ

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

指数の規則を適用する:

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

(27 x^{6})^{\frac{2}{3}} = 2 7^{\frac{2}{3}} (x^{6})^{\frac{2}{3}}

= 2 7^{\frac{2}{3}} (x^{6})^{\frac{2}{3}}

2 7^{\frac{2}{3}} = 9

= 9 (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}}

= 9 x^{6 \cdot \frac{2}{3}}

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

= 9 x^{4}