First, have a little knowledge of amplifiers and wiring them and most importantly have all the tools to do it. Do not attempt installing it yourself if you do not know anything about wiring amps. It is pretty hard to do for a person with little knowledge. For step by step help go to this url, it is very helpful http://www.caraudiohelp.com/how_to_install_a_car_amp/how_to_install_a_car_amp .htm
Amplifiers and better speakers. But amplifiers are a must.
Local laws may vary. Typicaly noise laws are to not make a lot of noise after 10 pm. You can check your city code.
You shouldn't need to change your battery. If those amps you've installed are huge, multi-thousand Watt monsters, then you may want to look at installing one or two 1 Farad capacitors, and replace/upgrade your alternator.
There are some car amplifiers that mount in the dash. Car amplifiers can be mount in the trunk, under the seat...
Yes, infinity makes good car amplifiers.
Car amplifiers can be as loud as those which have more than 1000 watt power. The Loudest TL-1021 series from WIKIO are some of the loud car amplifiers. Audio Assault also comes out with car amplifiers of 1000 W.
Yes -- speakers and amplifiers should be properly matched by power rating and impedance to avoid damage to either component.
Pioneer's amplifiers are one of the most durable.
There are many retailers where one can purchase car audio amplifiers. Edmunds, Best Buy, Amazon, Crutchfield and eBay all sell car audio amplifiers for people to purchase.
The cost of car amplifiers is going to vary based on a number of things such as the brand, the car it will be going in, and what amplifier level is needed.
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That depend of personal taste. Classic look of Pioneer's amplifiers are the coolest to me.