簡約 (9x^4)^{1/2}

解

簡約

(9 x^{4})^{\frac{1}{2}}

3 x^{2}

解答ステップ

(9 x^{4})^{\frac{1}{2}}

指数の規則を適用する:

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

(9 x^{4})^{\frac{1}{2}} = 9^{\frac{1}{2}} (x^{4})^{\frac{1}{2}}

= 9^{\frac{1}{2}} (x^{4})^{\frac{1}{2}}

9^{\frac{1}{2}} = 3

= 3 (x^{4})^{\frac{1}{2}}

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{1}{2}} = x^{4 \cdot \frac{1}{2}}

= 3 x^{4 \cdot \frac{1}{2}}

4 \cdot \frac{1}{2} = 2

= 3 x^{2}