簡約 \sqrt[6]{(2x^2)^2}

解

簡約

6 (2 x^{2})^{2}

32 3 x^{2}

解答ステップ

6 (2 x^{2})^{2}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

= ((2 x^{2})^{2})^{\frac{1}{6}}

指数の規則を適用する:

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

, 以下を想定

a \geq 0

= (2 x^{2})^{2 \cdot \frac{1}{6}}

2 \cdot \frac{1}{6} = \frac{1}{3}

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

a^{\frac{1}{n}} = n a

= 3 2 x^{2}

累乗根の規則を適用する:

n ab = n a n b,

, 以下を想定

a \geq 0, b \geq 0

= 32 3 x^{2}