簡約 (27\sqrt[3]{z^2})^{1/3}

解

簡約

(27 3 z^{2})^{\frac{1}{3}}

3 z^{\frac{2}{9}}

解答ステップ

(27 3 z^{2})^{\frac{1}{3}}

指数の規則を適用する:

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

(27 3 z^{2})^{\frac{1}{3}} = 2 7^{\frac{1}{3}} (3 z^{2})^{\frac{1}{3}}

= 2 7^{\frac{1}{3}} (3 z^{2})^{\frac{1}{3}}

2 7^{\frac{1}{3}} = 3

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

累乗根の規則を適用する:

n a^{m} = a^{\frac{m}{n}},

, 以下を想定

a \geq 0

3 z^{2} = z^{\frac{2}{3}}

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

(z^{\frac{2}{3}})^{\frac{1}{3}} = z^{\frac{2}{3} \cdot \frac{1}{3}}

= 3 z^{\frac{2}{3} \cdot \frac{1}{3}}

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

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