簡約 (16x^4)^{3/4}

解

簡約

(16 x^{4})^{\frac{3}{4}}

8 x^{3}

解答ステップ

(16 x^{4})^{\frac{3}{4}}

指数の規則を適用する:

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

(16 x^{4})^{\frac{3}{4}} = 1 6^{\frac{3}{4}} (x^{4})^{\frac{3}{4}}

= 1 6^{\frac{3}{4}} (x^{4})^{\frac{3}{4}}

1 6^{\frac{3}{4}} = 8

= 8 (x^{4})^{\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

(x^{4})^{\frac{3}{4}} = x^{4 \cdot \frac{3}{4}}

= 8 x^{4 \cdot \frac{3}{4}}

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

= 8 x^{3}