Car subwoofer powered by mains voltage
There is only one good reason to power a 500+ Watt car amp from AC mains: to save money by using what you have.  From an electrical and practical point of view, it's silly.

Assuming you want to save money then the best way would be to use a car battery plus battery charger. The battery provides energy storage for the peaks but the charger keeps it going. There are lots of things wrong with this approach. The most important one is dealing with the potential for the battery to vent corrosive gases. But it will provide 1600 Watts for short times. Another issue is the cost of a battery and charger could cost as much as the correct solution-- unless you have it already.

The correct solution is to buy a real amp that runs off of the AC mains. It will be plenty powerful, have better audio quality, and be more reliable.  Something like the QSC G5 or G7 amp. (Disclaimer : I work for QSC, so I'm biased!)