簡約 (28^{3/5})^{5/6}

解

簡約

(2 8^{\frac{3}{5}})^{\frac{5}{6}}

2 \cdot 7^{\frac{1}{2}}

十進法表記

5.29150 \dots

解答ステップ

(2 8^{\frac{3}{5}})^{\frac{5}{6}}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}, a \geq 0

= 2 8^{\frac{3}{5} \cdot \frac{5}{6}}

\frac{3}{5} \cdot \frac{5}{6} = \frac{1}{2}

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

以下の素因数分解:

28 : 2^{2} \cdot 7

= (2^{2} \cdot 7)^{\frac{1}{2}}

指数の規則を適用する:

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

(2^{2} \cdot 7)^{\frac{1}{2}} = (2^{2})^{\frac{1}{2}} \cdot 7^{\frac{1}{2}}

= (2^{2})^{\frac{1}{2}} \cdot 7^{\frac{1}{2}}

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

= 2 \cdot 7^{\frac{1}{2}}