簡約 (4c^5d^2)^{3/2}

解

簡約

(4 c^{5} d^{2})^{\frac{3}{2}}

8 c^{\frac{15}{2}} d^{3}

解答ステップ

(4 c^{5} d^{2})^{\frac{3}{2}}

指数の規則を適用する:

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

(4 c^{5} d^{2})^{\frac{3}{2}} = 4^{\frac{3}{2}} (c^{5})^{\frac{3}{2}} (d^{2})^{\frac{3}{2}}

= 4^{\frac{3}{2}} (c^{5})^{\frac{3}{2}} (d^{2})^{\frac{3}{2}}

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

= 8 (c^{5})^{\frac{3}{2}} (d^{2})^{\frac{3}{2}}

簡素化

(c^{5})^{\frac{3}{2}} : c^{\frac{15}{2}}

= 8 c^{\frac{15}{2}} (d^{2})^{\frac{3}{2}}

簡素化

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

= 8 c^{\frac{15}{2}} d^{3}