簡約 9^{3/7}*3^{1/7}

解

簡約

9^{\frac{3}{7}} \cdot 3^{\frac{1}{7}}

3

解答ステップ

9^{\frac{3}{7}} \cdot 3^{\frac{1}{7}}

整数を因数分解する

9 = 3^{2}

= (3^{2})^{\frac{3}{7}} \cdot 3^{\frac{1}{7}}

指数の規則を適用する:

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

(3^{2})^{\frac{3}{7}} = 3^{2 \cdot \frac{3}{7}}

= 3^{2 \cdot \frac{3}{7}} \cdot 3^{\frac{1}{7}}

改良

= 3^{\frac{6}{7}} \cdot 3^{\frac{1}{7}}

指数の規則を適用する:

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

3^{\frac{6}{7}} \cdot 3^{\frac{1}{7}} = 3^{\frac{6}{7} + \frac{1}{7}}

= 3^{\frac{6}{7} + \frac{1}{7}}

結合

\frac{6}{7} + \frac{1}{7} : 1

= 3^{1}

規則を適用

a^{1} = a

= 3