簡約 1/4 (4)^{3/2}

解

簡約

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

2

解答ステップ

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

数を因数に分解する:

4 = 2^{2}

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

指数の規則を適用する:

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

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

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

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

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

2^{3} = 8

= \frac{1}{4} \cdot 8

\frac{1}{4} \cdot 8 = 2

= 2