簡約 \sqrt[5]{96}*\sqrt[3]{3}

解

簡約

596 \cdot 33

2 15 3^{8}

十進法表記

3.59330 \dots

解答ステップ

59633

596 = 253

= 25333

累乗根の規則を適用する:

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

53 = 3^{\frac{1}{5}}

= 2 \cdot 3^{\frac{1}{5}} 33

累乗根の規則を適用する:

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

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

= 2 \cdot 3^{\frac{1}{5}} \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}{5}} \cdot 3^{\frac{1}{3}} = 3^{\frac{1}{5} + \frac{1}{3}}

= 2 \cdot 3^{\frac{1}{5} + \frac{1}{3}}

\frac{1}{5} + \frac{1}{3} = \frac{8}{15}

= 2 \cdot 3^{\frac{8}{15}}

= 3^{\frac{8}{15}} \cdot 2

3^{\frac{8}{15}} = 15 3^{8}

= 15 3^{8} \cdot 2

= 2 15 3^{8}