簡約 48^{1/4}

解

簡約

4 8^{\frac{1}{4}}

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

十進法表記

2.63214 \dots

解答ステップ

4 8^{\frac{1}{4}}

以下の素因数分解:

48 : 2^{4} \cdot 3

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

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

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

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