Chicken Egg Problem - Probability

I stumbled over this probability problem, the solution is explained in the textbook and i am able to follow it, until the point below where i don’t see how they arrive at the next line. I just have no clue.

The closest I get is this

• Welcome to CV, Petra! If you click "edit" to the lower left of your question, and add the [self-study] tag this question will likely get more attention. – Alexis Aug 29 '18 at 20:27

The remaining step to get what you need is that $$e^{-\lambda}=e^{-\lambda p}\cdot e^{-\lambda q}$$ if $p+q=1$.