What is e^{(x^2)/2}e^{-x^2} ?

The solution to e^{(x^2)/2}e^{-x^2} is 1/(e^{\frac{x^2){2}}}

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simplify e^{(x^2)/2}e^{-x^2}

simplify

e^{\frac{x ^{2}}{2}} e^{- x^{2}}

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

Solution steps

e^{\frac{x ^{2}}{2}} e^{- x^{2}}

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply:

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

= \frac{e ^{\frac{x ^{2}}{2}}}{e ^{x^{2}}}

Apply exponent rule:

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

\frac{e ^{\frac{x ^{2}}{2}}}{e ^{x^{2}}} = e^{\frac{x ^{2}}{2} - x^{2}} = e^{- \frac{x ^{2}}{2}}

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

e^{- 2} x

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What is e^{(x^2)/2}e^{-x^2} ?
The solution to e^{(x^2)/2}e^{-x^2} is 1/(e^{\frac{x^2){2}}}