簡約 (1/2 x^3)^2

解

簡約

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

\frac{x ^{6}}{4}

解答ステップ

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

指数の規則を適用する:

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

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

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

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

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

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

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

数を乗じる:

3 \cdot 2 = 6

= \frac{1}{4} x^{6}

簡素化

\frac{1}{4} x^{6} : \frac{x ^{6}}{4}

= \frac{x ^{6}}{4}