Could I plug a mic directly into the input of a powered speaker without any problems? Like for gigs where we don't need to mic everything, just need vocals, it would be nice to just bring a mic and a speaker, but I don't know if it would work without any problems. I don't want to try it in fear of messing the speakers up, so I figure I'd ask this forum. thanks.

I've never heard of it causing problems. You wouldn't have any eq capabilities, but i think it would be find. It is an Input after all. So it shouldn't damage the mic. It certainly won't hurt he speaker.
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You mean like a PA?
Now it's 1984
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It's the suede denim secret police
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yeah mate thats fine - probably the cheapest way of getting vocals heard without sounding like crap