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My buddy who I drum for his band has a pretty new jbl PA. He has a makie 12 channel mixer he hooks it up to. We moved the gear from my basement to his garage. Got everything set and and the sound from the PA was a weak. Like one of the speakers wasn't working. As we started trying stuff I shut down the mixing board while still connected to the speakers and the PA was still plugged in. The speakers are powered on there own. I don't believe I could mess something up by turning off the mixer first since the mixer doesn't send power to the speakers. Is this correct? It's all under warranty so it's all ok. Just wanted to know if I did mess up something.

Unlikely that you did, but general rule of thumb is always turn off the speakers first.

Mixers and powered speakers can be tricky to setup. Probably just a step along the setup was missed somewhere. As for shutting the mixer off with the speakers still on. If there was a "POP!" noise that was just the caps in the mixer discharging which is totally normal, it's the equivalent of your guitar amp making a pop noise through your cab when it shuts off. Playing loud distorted music through the speaker would cause more damage than the voltage of discharging caps, unless it was drastic cap failure, but that's rare.