簡約 (243x^5)^{4/5}

解

簡約

(243 x^{5})^{\frac{4}{5}}

81 x^{4}

解答ステップ

(243 x^{5})^{\frac{4}{5}}

指数の規則を適用する:

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

(243 x^{5})^{\frac{4}{5}} = 24 3^{\frac{4}{5}} (x^{5})^{\frac{4}{5}}

= 24 3^{\frac{4}{5}} (x^{5})^{\frac{4}{5}}

24 3^{\frac{4}{5}} = 81

= 81 (x^{5})^{\frac{4}{5}}

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

= 81 x^{5 \cdot \frac{4}{5}}

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

= 81 x^{4}