簡約 \sqrt[3]{3}*\sqrt[3]{3}

解

簡約

33 \cdot 33

3 3^{2}

十進法表記

2.08008 \dots

解答ステップ

3333

累乗根の規則を適用する:

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

33 = 3^{\frac{1}{3}}

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

指数の規則を適用する:

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

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

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

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

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

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

= 3 3^{2}