簡約 (64y^{100})^{1/2}

解

簡約

(64 y^{100})^{\frac{1}{2}}

8 y^{50}

解答ステップ

(64 y^{100})^{\frac{1}{2}}

指数の規則を適用する:

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

(64 y^{100})^{\frac{1}{2}} = 6 4^{\frac{1}{2}} (y^{100})^{\frac{1}{2}}

= 6 4^{\frac{1}{2}} (y^{100})^{\frac{1}{2}}

6 4^{\frac{1}{2}} = 8

= 8 (y^{100})^{\frac{1}{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

(y^{100})^{\frac{1}{2}} = y^{100 \cdot \frac{1}{2}}

= 8 y^{100 \cdot \frac{1}{2}}

100 \cdot \frac{1}{2} = 50

= 8 y^{50}