簡約 e^{-1/2 (1/2)^2 1/2}

解

簡約

e^{- \frac{1}{2} (\frac{1}{2})^{2} \frac{1}{2}}

\frac{1}{16 e}

十進法表記

0.93941 \dots

解答ステップ

e^{- \frac{1}{2} (\frac{1}{2})^{2} \frac{1}{2}}

指数の規則を適用する:

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

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

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

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

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

= \frac{1}{e ^{\frac{1}{2 ^{4}}}}

2^{4} = 16

= \frac{1}{16 e}