I should be able to run just about anything with that inverter. It's a "modified sine wave" inverter, i.e. the cheaper kind, and they say you should use that kind of inverter to power things with electric motors, but in practice I've read that they work just fine, especially with an inverter this powerful. The other, more expensive kind, is called a "pure sine wave" inverter. They're much more expensive.
I went with the 2000 watt version because I'm hoping to be able to run a heat gun from the inverter. I have a 1500w heat gun so we'll see if it works.
Best way to install them is just like an amplifier. Heavy gauge cable from the battery straight to the inverter with a fuse in between (close to the battery). Shortest ground possible. That why I just hooked it up with the amp–a distribution block splits the power we ran for the amp and also powers the inverter (though I have now connected the cables yet). I just wouldn't recommend trying to use the inverter and the car stereo at the same time.
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