簡約 (9/2 x^{1/2})^2

解

簡約

(\frac{9}{2} x^{\frac{1}{2}})^{2}

\frac{81 x}{4}

解答ステップ

(\frac{9}{2} x^{\frac{1}{2}})^{2}

指数の規則を適用する:

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

(\frac{9}{2} x^{\frac{1}{2}})^{2} = (\frac{9}{2})^{2} (x^{\frac{1}{2}})^{2}

= (\frac{9}{2})^{2} (x^{\frac{1}{2}})^{2}

(\frac{9}{2})^{2} = \frac{81}{4}

= \frac{81}{4} (x^{\frac{1}{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

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

= \frac{81}{4} x^{\frac{1}{2} \cdot 2}

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

= \frac{81}{4} x^{1}

指数の規則を適用する:

a^{1} = a

x^{1} = x

= \frac{81}{4} x

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{81 x}{4}