簡約 \sqrt[3]{x^2}*\sqrt[3]{x^2}

解

簡約

3 x^{2} \cdot 3 x^{2}

3 x^{4}

解答ステップ

3 x^{2} 3 x^{2}

累乗根の規則を適用する:

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

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

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

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

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

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

\frac{1}{3} + \frac{1}{3} = \frac{2}{3}

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

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^{2 \cdot \frac{2}{3}}

2 \cdot \frac{2}{3} = \frac{4}{3}

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

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

= 3 x^{4}