簡約 (9^{2/3})(3)(3^{2/3})

解

簡約

(9^{\frac{2}{3}}) (3) (3^{\frac{2}{3}})

27

解答ステップ

(9^{\frac{2}{3}}) (3) (3^{\frac{2}{3}})

(9^{\frac{2}{3}}) (3) (3^{\frac{2}{3}}) = 9^{\frac{2}{3}} \cdot 3 \cdot 3^{\frac{2}{3}}

= 9^{\frac{2}{3}} \cdot 3 \cdot 3^{\frac{2}{3}}

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

= 9^{\frac{2}{3}} \cdot 3^{\frac{5}{3}}

整数を因数分解する

9 = 3^{2}

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

指数の規則を適用する:

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

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

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

改良

= 3^{\frac{4}{3}} \cdot 3^{\frac{5}{3}}

指数の規則を適用する:

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

3^{\frac{4}{3}} \cdot 3^{\frac{5}{3}} = 3^{\frac{4}{3} + \frac{5}{3}}

= 3^{\frac{4}{3} + \frac{5}{3}}

結合

\frac{4}{3} + \frac{5}{3} : 3

= 3^{3}

3^{3} = 27

= 27