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

The solution to 1/(sqrt(2pi))e^{-1/2*1^2} is 1/(sqrt(2)\sqrt{pi)sqrt(e)}

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

simplify

\frac{1}{2 π} e^{- \frac{1}{2} \cdot 1^{2}}

\frac{1}{2 π e}

Decimal Notation

0.24197 \dots

Solution steps

\frac{1}{2 π} e^{- \frac{1}{2} \cdot 1^{2}}

Apply exponent rule:

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

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

Apply rule

1^{a} = 1

1^{2} = 1

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

\frac{1}{2 π} = \frac{1}{2 π}

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

Multiply:

\frac{1}{2} \cdot 1 = \frac{1}{2}

= \frac{1}{e} \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}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 π e}

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What is 1/(sqrt(2pi))e^{-1/2*1^2} ?
The solution to 1/(sqrt(2pi))e^{-1/2*1^2} is 1/(sqrt(2)\sqrt{pi)sqrt(e)}