簡約 (\sqrt[3]{\sqrt[7]{sqrt(a^2b^3)}})^8

解

簡約

3 7 a^{2} b^{3}^{8}

3 (7 b a^{2} b^{2})^{8}

解答ステップ

3 7 a^{2} b^{3}^{8}

指数の規則を適用する:

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

3 7 a^{2} b^{3}^{6 + 2} = 3 7 a^{2} b^{3}^{6} 3 7 a^{2} b^{3}^{2}

= 3 7 a^{2} b^{3}^{6} 3 7 a^{2} b^{3}^{2}

簡素化

3 7 a^{2} b^{3}^{6} : 3 7 a^{2} b^{3}^{3}^{2}

= 3 7 a^{2} b^{3}^{3}^{2} 3 7 a^{2} b^{3}^{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 7 a^{2} b^{3}^{3} = 7 a^{2} b^{3}

= (7 a^{2} b^{3})^{2} 3 7 a^{2} b^{3}^{2}

簡素化

3 7 a^{2} b^{3}^{2} : (7 a^{2} b^{3})^{\frac{2}{3}}

= (7 a^{2} b^{3})^{2} (7 a^{2} b^{3})^{\frac{2}{3}}

指数の規則を適用する:

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

(7 a^{2} b^{3})^{2} (7 a^{2} b^{3})^{\frac{2}{3}} = (7 a^{2} b^{3})^{2 + \frac{2}{3}}

= (7 a^{2} b^{3})^{2 + \frac{2}{3}}

2 + \frac{2}{3} = \frac{8}{3}

= (7 a^{2} b^{3})^{\frac{8}{3}}

a^{2} b^{3} = b a^{2} b^{2}

= (7 b a^{2} b^{2})^{\frac{8}{3}}

(7 b a^{2} b^{2})^{\frac{8}{3}} = 3 (7 b a^{2} b^{2})^{8}

= 3 (7 b a^{2} b^{2})^{8}