簡約 2^{1/3}4^{1/6}8^{1/9}

解

簡約

2^{\frac{1}{3}} \cdot 4^{\frac{1}{6}} \cdot 8^{\frac{1}{9}}

2

解答ステップ

2^{\frac{1}{3}} \cdot 4^{\frac{1}{6}} \cdot 8^{\frac{1}{9}}

4^{\frac{1}{6}} = 2^{\frac{1}{3}}

= 2^{\frac{1}{3}} \cdot 2^{\frac{1}{3}} \cdot 8^{\frac{1}{9}}

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

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

指数の規則を適用する:

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

2^{\frac{1}{3}} \cdot 2^{\frac{1}{3}} \cdot 2^{\frac{1}{3}} = 2^{\frac{1}{3} + \frac{1}{3} + \frac{1}{3}}

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

\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1

= 2^{1}

指数の規則を適用する:

a^{1} = a

= 2