# Simple exponential expand **URL:** \ **Category:** Questions\ **Tags:** algebra\ **Created:** [March 9, 2025, 10:55pm UTC](https://community.wolfram.com/t/simple-exponential-expand/25227 "2025-03-09T22:55:27Z")\ **Posts on this page:** 3\ **Page:** 1
**Author:** ![hlyr314](https://avatars.discourse-cdn.com/v4/letter/h/e47c2d/32.png) [@hlyr314](https://community.wolfram.com/u/hlyr314)\ **Post date:** [March 9, 2025, 10:55pm UTC](https://community.wolfram.com/t/simple-exponential-expand/25227/1 "2025-03-09T22:55:27Z")
Is there a way to expand an exponential of a sum to a product of exponentials? Example: ``` Exp[a+b] ``` I want Mathematica to expand it to `Exp[a]*Exp[b]`. In my example, the full expression is `Exp[a+b]+c*Exp[a+d]` and I want to factor with respect to `Exp[a]` and expand to trig the terms `Exp[b]` and `Exp[d]`, where b and d are imaginary numbers. Thanks! ---
**Author:** ![mroge02](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/mroge02/32/28775_2.png) [@mroge02](https://community.wolfram.com/u/mroge02)\ **Post date:** [March 10, 2025, 1:24am UTC](https://community.wolfram.com/t/simple-exponential-expand/25227/2 "2025-03-10T01:24:04Z")
Since `Exp[a] Exp[b]` automatically evaluates to `Power[E, Plus[a, b]]`, it’s impossible to keep `Exp[a] Exp[b]` as is, unless you use `Hold[]` or `HoldForm[]`. On the other hand, we have this: ``` Factor[Exp[a + b] + c Exp[a + d]] (* E^a (E^b + c E^d) *) ``` If a, b, c, d have numeric values, then you have to take a more manual approach, since the numbers will combine with one another. Try the following: ``` Exp[a] Expand[(Exp[a + b] + c Exp[a + d])/Exp[a]] ``` ---
**Author:** ![gianlucagorni](https://avatars.discourse-cdn.com/v4/letter/g/ec9cab/32.png) [@gianlucagorni](https://community.wolfram.com/u/gianlucagorni)\ **Post date:** [March 11, 2025, 9:41am UTC](https://community.wolfram.com/t/simple-exponential-expand/25227/3 "2025-03-11T09:41:54Z")
Just one variation: ``` Exp[a + b] + c Exp[a + d] /. a -> Log[Defer[E^a]] ```