簡約 sqrt(3)\sqrt[3]{3^2}\sqrt[4]{3^3}

解

簡約

3 \cdot 3 3^{2} \cdot 4 3^{3}

3 \cdot 3^{\frac{5}{12}} 3

十進法表記

8.21263 \dots

解答ステップ

3 3 3^{2} 4 3^{3}

3 3^{2} : 3^{\frac{2}{3}}

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

4 3^{3} : 3^{\frac{3}{4}}

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

指数の規則を適用する:

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

3^{\frac{2}{3}} \cdot 3^{\frac{3}{4}} = 3^{\frac{2}{3} + \frac{3}{4}}

= 3 \cdot 3^{\frac{2}{3} + \frac{3}{4}}

3^{\frac{2}{3} + \frac{3}{4}} = 3 \cdot 3^{\frac{5}{12}}

= 3 \cdot 3^{\frac{5}{12}} 3