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I am in the middle of a stats-related proof and got stuck in an algebraic manipulation.

The source formula goes $$e^{tn}(pe^{-t}+q)^n,$$ and my target result is to simplify that into $$(qe^t+p)^n.$$ I'm not sure how to manipulate it.

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Hints:

$e^{tn}=(e^t)^n$;

and $(ab)^n=a^nb^n$.

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