簡約 \sqrt[5]{3^3}*(\sqrt[15]{3^2})^3

解

簡約

5 3^{3} \cdot (15 3^{2})^{3}

3

解答ステップ

5 3^{3} (15 3^{2})^{3}

5 3^{3} : 3^{\frac{3}{5}}

= 3^{\frac{3}{5}} (15 3^{2})^{3}

15 3^{2} : 3^{\frac{2}{15}}

= 3^{\frac{3}{5}} (3^{\frac{2}{15}})^{3}

(3^{\frac{2}{15}})^{3} = 3^{\frac{2}{5}}

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

指数の規則を適用する:

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

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

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

結合

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

= 3^{1}

規則を適用

a^{1} = a

= 3