簡約 (\sqrt[3]{1347/4})^2

解

簡約

(3 \frac{1347}{4})^{2}

(\frac{1347}{4})^{\frac{2}{3}}

十進法表記

48.40293 \dots

解答ステップ

(3 \frac{1347}{4})^{2}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

= ((\frac{1347}{4})^{\frac{1}{3}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (\frac{1347}{4})^{\frac{1}{3} \cdot 2}

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

= (\frac{1347}{4})^{\frac{2}{3}}