簡約 1/(sqrt(2(pi)(1)^2))e^{(-((4)^2)/2)}

解

簡約

\frac{1}{2 ( π ) ( 1 ) ^{2}} e^{(- \frac{( 4 ) ^{2}}{2})}

\frac{1}{2 ^{\frac{1}{2}} e ^{8} π ^{\frac{1}{2}}}

十進法表記

0.00013 \dots

解答ステップ

\frac{1}{2 ( π ) ( 1 ) ^{2}} e^{(- \frac{( 4 ) ^{2}}{2})}

指数の規則を適用する:

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

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

規則を適用

1^{a} = 1

1^{2} = 1

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

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

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

\frac{1}{e ^{\frac{4 ^{2}}{2}}} = \frac{1}{e ^{2^{3}}}

= \frac{1}{e ^{2^{3}}} \cdot \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

分数を乗じる:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}} e ^{2^{3}}}

数を乗じる:

1 \cdot 1 = 1

= \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}} e ^{2^{3}}}

2^{3} = 8

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