簡約 (8a^6b^{3/2})^{2/3}

解

簡約

(8 a^{6} b^{\frac{3}{2}})^{\frac{2}{3}}

4 a^{4} b

解答ステップ

(8 a^{6} b^{\frac{3}{2}})^{\frac{2}{3}}

指数の規則を適用する:

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

(8 a^{6} b^{\frac{3}{2}})^{\frac{2}{3}} = 8^{\frac{2}{3}} (a^{6})^{\frac{2}{3}} (b^{\frac{3}{2}})^{\frac{2}{3}}

= 8^{\frac{2}{3}} (a^{6})^{\frac{2}{3}} (b^{\frac{3}{2}})^{\frac{2}{3}}

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

= 4 (a^{6})^{\frac{2}{3}} (b^{\frac{3}{2}})^{\frac{2}{3}}

簡素化

(a^{6})^{\frac{2}{3}} : a^{4}

= 4 a^{4} (b^{\frac{3}{2}})^{\frac{2}{3}}

簡素化

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

= 4 a^{4} b