簡約 (\sqrt[3]{a^2b^4})^5

解

簡約

(3 a^{2} b^{4})^{5}

3 a^{10} 3 b^{20}

解答ステップ

(3 a^{2} b^{4})^{5}

指数の規則を適用する:

a^{b + c} = a^{b} \cdot a^{c}

(3 a^{2} b^{4})^{3 + 2} = (3 a^{2} b^{4})^{3} (3 a^{2} b^{4})^{2}

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

指数の規則を適用する:

(n a)^{n} = a,

, 以下を想定

n i s o dd or a \geq 0

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

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

簡素化

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

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

簡素化

a^{2} a^{\frac{4}{3}} : a^{\frac{10}{3}}

= a^{\frac{10}{3}} b^{4} b^{\frac{8}{3}}

簡素化

b^{4} b^{\frac{8}{3}} : b^{\frac{20}{3}}

= a^{\frac{10}{3}} b^{\frac{20}{3}}

a^{\frac{10}{3}} = 3 a^{10}

= 3 a^{10} 3 b^{20}

b^{\frac{20}{3}} = 3 b^{20}

= 3 a^{10} 3 b^{20}