Where is the exit button?

You can close it the same way you close stock player (back button or home).

Poweramp player service doesn't do any job if it's paused. 
Poweramp player service asks android to stop itself after 30 seconds of idle.

Poweramp has a Stop button (long press the pause/play does that), though that has nothing to do with the process or background running and it's not necessary to press this if you just want to exit Poweramp.

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