簡約 (12/10000)*2.72^{-(25/22)}

解

簡約

(\frac{12}{10000}) \cdot 2.7 2^{- (\frac{25}{22})}

\frac{3}{1360 \cdot 5 ^{\frac{8}{11}} \cdot 6 8 ^{\frac{3}{22}}}

十進法表記

0.00038 \dots

解答ステップ

(\frac{12}{10000}) \cdot 2.7 2^{- (\frac{25}{22})}

(\frac{12}{10000}) \cdot 2.7 2^{- (\frac{25}{22})} = \frac{12}{10000} \cdot 2.7 2^{- \frac{25}{22}}

= \frac{12}{10000} \cdot 2.7 2^{- \frac{25}{22}}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

2.7 2^{- \frac{25}{22}} = \frac{1}{2.7 2 ^{\frac{25}{22}}}

= \frac{12}{10000} \cdot \frac{1}{2.7 2 ^{\frac{25}{22}}}

2.72 = \frac{68}{25}

= \frac{12}{10000} \cdot \frac{1}{( \frac{68}{25} ) ^{\frac{25}{22}}}

\frac{1}{( \frac{68}{25} ) ^{\frac{25}{22}}} = \frac{25 \cdot 5 ^{\frac{3}{11}}}{68 \cdot 6 8 ^{\frac{3}{22}}}

= \frac{12}{10000} \cdot \frac{25 \cdot 5 ^{\frac{3}{11}}}{68 \cdot 6 8 ^{\frac{3}{22}}}

キャンセル

\frac{12}{10000} : \frac{3}{2500}

= \frac{3}{2500} \cdot \frac{25 \cdot 5 ^{\frac{3}{11}}}{68 \cdot 6 8 ^{\frac{3}{22}}}

\frac{3}{2500} \cdot \frac{25 \cdot 5 ^{\frac{3}{11}}}{68 \cdot 6 8 ^{\frac{3}{22}}} = \frac{3}{1360 \cdot 5 ^{\frac{8}{11}} \cdot 6 8 ^{\frac{3}{22}}}

= \frac{3}{1360 \cdot 5 ^{\frac{8}{11}} \cdot 6 8 ^{\frac{3}{22}}}