簡約 \sqrt[9]{\sqrt[3]{x^2*x^2}}

解

簡約

9 3 x^{2} \cdot x^{2}

27 x^{4}

解答ステップ

9 3 x^{2} x^{2}

累乗根の規則を適用する:

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

= ((x^{2} x^{2})^{\frac{1}{3}})^{\frac{1}{9}}

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} x^{2})^{\frac{1}{3} \cdot \frac{1}{9}}

\frac{1}{3} \cdot \frac{1}{9} = \frac{1}{27}

= (x^{2} x^{2})^{\frac{1}{27}}

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

= 27 x^{2} x^{2}

簡素化

x^{2} x^{2} : x^{4}

= 27 x^{4}