簡約 14252(0.5)^{40/32}

解

簡約

14252 (0.5)^{\frac{40}{32}}

2^{\frac{3}{4}} \cdot 3563

十進法表記

5992.22785 \dots

解答ステップ

14252 \cdot 0. 5^{\frac{40}{32}}

0.5 = \frac{1}{2}

= 14252 (\frac{1}{2})^{\frac{40}{32}}

共通因数を約分する:

8

= 14252 (\frac{1}{2})^{\frac{5}{4}}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{1}{2})^{\frac{5}{4}} = \frac{1 ^{\frac{5}{4}}}{2 ^{\frac{5}{4}}}

= 14252 \cdot \frac{1 ^{\frac{5}{4}}}{2 ^{\frac{5}{4}}}

\frac{1 ^{\frac{5}{4}}}{2 ^{\frac{5}{4}}} = \frac{1}{2 \cdot 2 ^{\frac{1}{4}}}

= 14252 \cdot \frac{1}{2 \cdot 2 ^{\frac{1}{4}}}

14252 \cdot \frac{1}{2 \cdot 2 ^{\frac{1}{4}}} = 2^{\frac{3}{4}} \cdot 3563

= 2^{\frac{3}{4}} \cdot 3563