簡約 2/3 9^{3/2}

解

簡約

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

18

解答ステップ

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

数を因数に分解する:

9 = 3^{2}

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

指数の規則を適用する:

(a^{b})^{c} = a^{b c}, a \geq 0

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

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

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

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

3^{3} = 27

= \frac{2}{3} \cdot 27

\frac{2}{3} \cdot 27 = 18

= 18