簡約 9^{1/3}*81^{1/3}

解

簡約

9^{\frac{1}{3}} \cdot 8 1^{\frac{1}{3}}

9

解答ステップ

9^{\frac{1}{3}} \cdot 8 1^{\frac{1}{3}}

8 1^{\frac{1}{3}} = 3 \cdot 3^{\frac{1}{3}}

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

3 \cdot 3^{\frac{1}{3}} = 3^{\frac{4}{3}}

= 9^{\frac{1}{3}} \cdot 3^{\frac{4}{3}}

整数を因数分解する

9 = 3^{2}

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

指数の規則を適用する:

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

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

= 3^{2 \cdot \frac{1}{3}} \cdot 3^{\frac{4}{3}}

改良

= 3^{\frac{2}{3}} \cdot 3^{\frac{4}{3}}

指数の規則を適用する:

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

3^{\frac{2}{3}} \cdot 3^{\frac{4}{3}} = 3^{\frac{2}{3} + \frac{4}{3}}

= 3^{\frac{2}{3} + \frac{4}{3}}

結合

\frac{2}{3} + \frac{4}{3} : 2

= 3^{2}

3^{2} = 9

= 9