Does input voltage affect output power?

A higher power supply voltage will allow higher maximum power output.
Doubling the voltage from 12V to 24V could quadruple the maximum power output,
provided the amplifier can also supply the higher current needed for the higher power
to the load. This is because power = (V x V / R), and (2V x 2V /R) is four times larger.
 
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V squared by R, so yeah it'll go down by a lot. This is why most car amps have inverters as part of the power supply. Get one to get your supply back up to 24V for full power capability of this amp. I'm sure ebay has it.