簡約 (sqrt(x/2))^4

解

簡約

(\frac{x}{2})^{4}

\frac{x ^{2}}{4}

解答ステップ

(\frac{x}{2})^{4}

4

を書き換え

2 \cdot 2

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

指数の規則を適用する:

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

, 以下を想定

a \geq 0

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

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

指数の規則を適用する:

(n a)^{n} = a,

, 以下を想定

n i s o dd or a \geq 0

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

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

指数の規則を適用する:

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

= \frac{x ^{2}}{2 ^{2}}

2^{2} = 4

= \frac{x ^{2}}{4}