化简 \sqrt[6]{z}\sqrt[5]{z}\sqrt[12]{z^5}

解答

化简

6 z \cdot 5 z \cdot 12 z^{5}

30 z^{11} 12 z^{5}

求解步骤

6 z 5 z 12 z^{5}

6 z = z^{\frac{1}{6}}

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

= z^{\frac{1}{6}} z^{\frac{1}{5}} 12 z^{5}

使用指数法则:

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

z^{\frac{1}{6}} z^{\frac{1}{5}} = z^{\frac{1}{6} + \frac{1}{5}}

= z^{\frac{1}{6} + \frac{1}{5}} 12 z^{5}

\frac{1}{6} + \frac{1}{5} = \frac{11}{30}

= z^{\frac{11}{30}} 12 z^{5}

z^{\frac{11}{30}} = 30 z^{11}

= 30 z^{11} 12 z^{5}

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