What is 1/(sqrt(6pi))e^{-(x^2)/2} ?

The solution to 1/(sqrt(6pi))e^{-(x^2)/2} is 1/(6^{1/2)pi^{1/2}e^{(x^2)/2}}

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simplify 1/(sqrt(6pi))e^{-(x^2)/2}

simplify

\frac{1}{6 π} e^{- \frac{x ^{2}}{2}}

\frac{1}{6 ^{\frac{1}{2}} π ^{\frac{1}{2}} e ^{\frac{x ^{2}}{2}}}

Solution steps

\frac{1}{6 π} e^{- \frac{x ^{2}}{2}}

Apply exponent rule:

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

= \frac{1}{6 π} \cdot \frac{1}{e ^{\frac{x ^{2}}{2}}}

\frac{1}{6 π} = \frac{1}{6 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

= \frac{1}{6 ^{\frac{1}{2}} π ^{\frac{1}{2}}} \cdot \frac{1}{e ^{\frac{x ^{2}}{2}}}

Multiply fractions:

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

= \frac{1 \cdot 1}{6 ^{\frac{1}{2}} π ^{\frac{1}{2}} e ^{\frac{x ^{2}}{2}}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{6 ^{\frac{1}{2}} π ^{\frac{1}{2}} e ^{\frac{x ^{2}}{2}}}

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What is 1/(sqrt(6pi))e^{-(x^2)/2} ?
The solution to 1/(sqrt(6pi))e^{-(x^2)/2} is 1/(6^{1/2)pi^{1/2}e^{(x^2)/2}}