化简 sqrt(x)\sqrt[5]{x}

解答

化简

x 5 x

10 x^{7}

求解步骤

x 5 x

x = x^{\frac{1}{2}}

5 x = x^{\frac{1}{5}}

= x^{\frac{1}{2}} x^{\frac{1}{5}}

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

x^{\frac{1}{2}} x^{\frac{1}{5}} = x^{\frac{1}{2} + \frac{1}{5}}

= x^{\frac{1}{2} + \frac{1}{5}}

\frac{1}{2} + \frac{1}{5} = \frac{7}{10}

= x^{\frac{7}{10}}

x^{\frac{7}{10}} = 10 x^{7}

= 10 x^{7}

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