What is 1/(sqrt(2pi))e^{-0.5(-2)^2} ?

The solution to 1/(sqrt(2pi))e^{-0.5(-2)^2} is 0.05399…

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simplify 1/(sqrt(2pi))e^{-0.5(-2)^2}

simplify

\frac{1}{2 π} e^{- 0.5 (- 2)^{2}}

0.05399 \dots

Solution steps

\frac{1}{2 π} e^{- 0.5 (- 2)^{2}}

Apply exponent rule:

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

= \frac{1}{2 π} \cdot \frac{1}{e ^{(- 2)^{2} \cdot 0.5}}

\frac{1}{2 π} = \frac{1}{2 π}

= \frac{1}{e ^{(- 2)^{2} \cdot 0.5}} \cdot \frac{1}{2 π}

\frac{1}{e ^{0.5 (- 2)^{2}}} = \frac{1}{e ^{2^{2} \cdot 0.5}}

= \frac{1}{e ^{2^{2} \cdot 0.5}} \cdot \frac{1}{2 π}

Multiply fractions:

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

= \frac{1 \cdot 1}{2 π e ^{0.5 \cdot 2^{2}}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 π e ^{2^{2} \cdot 0.5}}

e^{0.5 \cdot 2^{2}} = e^{2}

= \frac{1}{2 e ^{2} π}

Convert element to a decimal form

2 = 1.41421 \dots

= \frac{1}{1.41421 \dots e ^{2} π}

Convert element to a decimal form

π = 1.77245 \dots

= \frac{1}{1.41421 \dots \cdot 1.77245 \dots e ^{2}}

Convert element to a decimal form

e^{2} = 7.38905 \dots

= \frac{1}{1.41421 \dots \cdot 1.77245 \dots \cdot 7.38905 \dots}

Multiply the numbers:

1.41421 \dots \cdot 1.77245 \dots \cdot 7.38905 \dots = 18.52161 \dots

= \frac{1}{18.52161 \dots}

Divide the numbers:

\frac{1}{18.52161 \dots} = 0.05399 \dots

= 0.05399 \dots

2 2^{\frac{1}{3}}

20 e^{- 0.2 (5)}

e^{z} e^{z}

4 7^{2}

(0)^{3} e^{- (0)}

What is 1/(sqrt(2pi))e^{-0.5(-2)^2} ?
The solution to 1/(sqrt(2pi))e^{-0.5(-2)^2} is 0.05399…