化简 (9u^4)^{1/2}

解答

化简

(9 u^{4})^{\frac{1}{2}}

3 u^{2}

求解步骤

(9 u^{4})^{\frac{1}{2}}

使用指数法则:

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

(9 u^{4})^{\frac{1}{2}} = 9^{\frac{1}{2}} (u^{4})^{\frac{1}{2}}

= 9^{\frac{1}{2}} (u^{4})^{\frac{1}{2}}

9^{\frac{1}{2}} = 3

= 3 (u^{4})^{\frac{1}{2}}

使用指数法则:

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

假定

a \geq 0

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

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

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

= 3 u^{2}

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