簡約 (1/2 t^2)^2

解

簡約

(\frac{1}{2} t^{2})^{2}

\frac{t ^{4}}{4}

解答ステップ

(\frac{1}{2} t^{2})^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(\frac{1}{2} t^{2})^{2} = (\frac{1}{2})^{2} (t^{2})^{2}

= (\frac{1}{2})^{2} (t^{2})^{2}

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

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

(t^{2})^{2} = t^{2 \cdot 2}

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

数を乗じる:

2 \cdot 2 = 4

= \frac{1}{4} t^{4}

簡素化

\frac{1}{4} t^{4} : \frac{t ^{4}}{4}

= \frac{t ^{4}}{4}