簡約 458(1/2)^{50/30}

解

簡約

458 (\frac{1}{2})^{\frac{50}{30}}

\frac{229}{2 ^{\frac{2}{3}}}

十進法表記

144.26096 \dots

解答ステップ

458 (\frac{1}{2})^{\frac{50}{30}}

指数の規則を適用する:

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

(\frac{1}{2})^{\frac{50}{30}} = \frac{1 ^{\frac{50}{30}}}{2 ^{\frac{50}{30}}}

= 458 \cdot \frac{1 ^{\frac{50}{30}}}{2 ^{\frac{50}{30}}}

1^{\frac{50}{30}} = 1

= 458 \cdot \frac{1}{2 ^{\frac{50}{30}}}

2^{\frac{50}{30}} = 2 \cdot 2^{\frac{2}{3}}

= 458 \cdot \frac{1}{2 \cdot 2 ^{\frac{2}{3}}}

458 \cdot \frac{1}{2 \cdot 2 ^{\frac{2}{3}}} = \frac{229}{2 ^{\frac{2}{3}}}

= \frac{229}{2 ^{\frac{2}{3}}}