簡約 (x^3y^2z^3)^{1/13}

解

簡約

(x^{3} y^{2} z^{3})^{\frac{1}{13}}

x^{\frac{3}{13}} y^{\frac{2}{13}} z^{\frac{3}{13}}

解答ステップ

(x^{3} y^{2} z^{3})^{\frac{1}{13}}

指数の規則を適用する:

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

(x^{3} y^{2} z^{3})^{\frac{1}{13}} = (x^{3})^{\frac{1}{13}} (y^{2})^{\frac{1}{13}} (z^{3})^{\frac{1}{13}}

= (x^{3})^{\frac{1}{13}} (y^{2})^{\frac{1}{13}} (z^{3})^{\frac{1}{13}}

簡素化

(x^{3})^{\frac{1}{13}} : x^{\frac{3}{13}}

= x^{\frac{3}{13}} (y^{2})^{\frac{1}{13}} (z^{3})^{\frac{1}{13}}

簡素化

(y^{2})^{\frac{1}{13}} : y^{\frac{2}{13}}

= x^{\frac{3}{13}} y^{\frac{2}{13}} (z^{3})^{\frac{1}{13}}

簡素化

(z^{3})^{\frac{1}{13}} : z^{\frac{3}{13}}

= x^{\frac{3}{13}} y^{\frac{2}{13}} z^{\frac{3}{13}}