簡約 (625a^8)^{3/4}

解

簡約

(625 a^{8})^{\frac{3}{4}}

125 a^{6}

解答ステップ

(625 a^{8})^{\frac{3}{4}}

指数の規則を適用する:

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

(625 a^{8})^{\frac{3}{4}} = 62 5^{\frac{3}{4}} (a^{8})^{\frac{3}{4}}

= 62 5^{\frac{3}{4}} (a^{8})^{\frac{3}{4}}

62 5^{\frac{3}{4}} = 125

= 125 (a^{8})^{\frac{3}{4}}

指数の規則を適用する:

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

, 以下を想定

a \geq 0

(a^{8})^{\frac{3}{4}} = a^{8 \cdot \frac{3}{4}}

= 125 a^{8 \cdot \frac{3}{4}}

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

= 125 a^{6}