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

The solution to e^{-(x^2)/(2a^2)}e^{-(x^2)/(2a^2)} is e^{-(x^2)/(a^2)}

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

simplify

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

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

Solution steps

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

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

Combine the fractions

- \frac{x ^{2}}{2 a ^{2}} - \frac{x ^{2}}{2 a ^{2}} : - \frac{x ^{2}}{a ^{2}}

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

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