簡約 \sqrt[4]{z}\sqrt[5]{z}\sqrt[10]{z^3}

解

簡約

4 z \cdot 5 z \cdot 10 z^{3}

20 z^{9} 10 z^{3}

解答ステップ

4 z 5 z 10 z^{3}

4 z = z^{\frac{1}{4}}

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

= z^{\frac{1}{4}} z^{\frac{1}{5}} 10 z^{3}

指数の規則を適用する:

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

z^{\frac{1}{4}} z^{\frac{1}{5}} = z^{\frac{1}{4} + \frac{1}{5}}

= z^{\frac{1}{4} + \frac{1}{5}} 10 z^{3}

\frac{1}{4} + \frac{1}{5} = \frac{9}{20}

= z^{\frac{9}{20}} 10 z^{3}

z^{\frac{9}{20}} = 20 z^{9}

= 20 z^{9} 10 z^{3}