簡約 (-4x^3)^{2/3}

解

簡約

(- 4 x^{3})^{\frac{2}{3}}

4^{\frac{2}{3}} x^{2}

解答ステップ

(- 4 x^{3})^{\frac{2}{3}}

指数の規則を適用する:

(- a)^{\frac{m}{n}} = (- 1)^{\frac{m}{n}} (a)^{\frac{m}{n}}

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

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

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

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

指数の規則を適用する:

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

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

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

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

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

乗算:

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

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