簡約 [(2^2)^{1/2}]^{1/3}*[(2^3)^{1/3}]^{1/2}

解

簡約

[(2^{2})^{\frac{1}{2}}]^{\frac{1}{3}} \cdot [(2^{3})^{\frac{1}{3}}]^{\frac{1}{2}}

2^{\frac{5}{6}}

十進法表記

1.78179 \dots

解答ステップ

[(2^{2})^{\frac{1}{2}}]^{\frac{1}{3}} [(2^{3})^{\frac{1}{3}}]^{\frac{1}{2}}

(2^{2})^{\frac{1}{2}} : 2

= [2]^{\frac{1}{3}} ((2^{3})^{\frac{1}{3}})^{\frac{1}{2}}

(2^{3})^{\frac{1}{3}} : 2

= [2]^{\frac{1}{3}} \cdot 2^{\frac{1}{2}}

指数の規則を適用する:

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

2^{\frac{1}{3}} \cdot 2^{\frac{1}{2}} = 2^{\frac{1}{3} + \frac{1}{2}}

= 2^{\frac{1}{3} + \frac{1}{2}}

結合

\frac{1}{3} + \frac{1}{2} : \frac{5}{6}

= 2^{\frac{5}{6}}