簡約 (8x^4y^5)^{2/3}

解

簡約

(8 x^{4} y^{5})^{\frac{2}{3}}

4 x^{\frac{8}{3}} y^{\frac{10}{3}}

解答ステップ

(8 x^{4} y^{5})^{\frac{2}{3}}

指数の規則を適用する:

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

(8 x^{4} y^{5})^{\frac{2}{3}} = 8^{\frac{2}{3}} (x^{4})^{\frac{2}{3}} (y^{5})^{\frac{2}{3}}

= 8^{\frac{2}{3}} (x^{4})^{\frac{2}{3}} (y^{5})^{\frac{2}{3}}

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

= 4 (x^{4})^{\frac{2}{3}} (y^{5})^{\frac{2}{3}}

簡素化

(x^{4})^{\frac{2}{3}} : x^{\frac{8}{3}}

= 4 x^{\frac{8}{3}} (y^{5})^{\frac{2}{3}}

簡素化

(y^{5})^{\frac{2}{3}} : y^{\frac{10}{3}}

= 4 x^{\frac{8}{3}} y^{\frac{10}{3}}