簡約 (5x^2y^{10})^{1/5}

解

簡約

(5 x^{2} y^{10})^{\frac{1}{5}}

5^{\frac{1}{5}} x^{\frac{2}{5}} y^{2}

解答ステップ

(5 x^{2} y^{10})^{\frac{1}{5}}

指数の規則を適用する:

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

(5 x^{2} y^{10})^{\frac{1}{5}} = 5^{\frac{1}{5}} (x^{2})^{\frac{1}{5}} (y^{10})^{\frac{1}{5}}

= 5^{\frac{1}{5}} (x^{2})^{\frac{1}{5}} (y^{10})^{\frac{1}{5}}

簡素化

(x^{2})^{\frac{1}{5}} : x^{\frac{2}{5}}

= 5^{\frac{1}{5}} x^{\frac{2}{5}} (y^{10})^{\frac{1}{5}}

簡素化

(y^{10})^{\frac{1}{5}} : y^{2}

= 5^{\frac{1}{5}} x^{\frac{2}{5}} y^{2}