What is e^{-r/a}*e^{-r/a} ?

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

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simplify e^{-r/a}*e^{-r/a}

simplify

e^{- \frac{r}{a}} \cdot e^{- \frac{r}{a}}

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

Solution steps

e^{- \frac{r}{a}} e^{- \frac{r}{a}}

Apply exponent rule:

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

e^{- \frac{r}{a}} e^{- \frac{r}{a}} = e^{- \frac{r}{a} - \frac{r}{a}}

= e^{- \frac{r}{a} - \frac{r}{a}}

Combine the fractions

- \frac{r}{a} - \frac{r}{a} : - \frac{2 r}{a}

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

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