簡約 6^{1/2}2^{1/4}1^{1/4}

解

簡約

6^{\frac{1}{2}} \cdot 2^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

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

十進法表記

2.91295 \dots

解答ステップ

6^{\frac{1}{2}} \cdot 2^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

指数の規則を適用する:

a^{m} b^{m} = (ab)^{m}

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

= 6^{\frac{1}{2}} (2 \cdot 1)^{\frac{1}{4}}

数を乗じる:

2 \cdot 1 = 2

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

整数を因数分解する

6 = 2 \cdot 3

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

指数の規則を適用する:

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

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

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

指数の規則を適用する:

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

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

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

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

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