Amplifier power ratings are leading when you decree if an amp will satisfy your system's needs or not. Amp manufacturer has to give out a power specification which clear and complete. Otherwise you are just guessing. An example of a good power amp spec for a 4 channel amp is:
"50watts X 4 Rms all channels driven continuously into 4 ohms with less than 0.1%Thd from 20Hz to 20kHz"
In Dash Double Din
Every part of that spec is meaningful and without any part of it the power rating is meaningless. Amp manufacturers do not give this much information always but you have to decree for yourself either they are hiding anything. Head unit power ratings are preponderant for being very misleading.
The "50watts" part is the one we see first and everything else matters how that "50watts" was measured. Having enough powerfull amp is what most citizen look for. However, other things come into play. If you are going to run a load less than 4 ohms, then the current ability of the amp is leading and most specs do not give a current capability. A power rating into 2 ohms can help though. If the power doubles into 2 ohms then the amp is built strongly enough that it can deliver enough current to drive a 2 ohm load. You may think that this is not leading if you are not going to drive 2 ohm loads but it is important. Speakers (woofers, midranges, tweeters, etc) are not purely resistive. They have capacitive and inductive properties as well. Depending on the music and your setup, the impedance may dip well below 4 ohms for a nominally 4 ohm speaker.
Whether you amp can yield current fast enough to reproduce the music clearly depends partially on the amp's slew rate, its damping factor and its current capability. Because of these these reasons 2 ohm power is leading even when driving 4 ohm speakers. I hope it is clear now that the amount of watts an amp can build is only one thing in determining either an amp is capable of the carrying out you want.
On a last note on this part of the spec, Ic is used by most head units for the built-in amp's output stage. Those chips can´t furnish enough current which is why even most amateurs know not drive subwoofers from a head unit. Real amps often have Ics in them as well but the output stages are approximately every time discrete, meaning they are made from transistors, resistors, capacitors and not integrated together inside tiny Ics.
The "X 4″ means that the amp has 4 output channels. The "Rms" stands for "root mean square" and is a formula of measuring an Ac waveform. Here it means that the power rating is not just a peak rating but continuous. "all channels driven" implies that the power determination was made with all channels driven to their maximum level at the same time. This means that the power furnish is mighty enough to allow all 4 output channels to make 50watts at the same time.
This is a the place where head unit specs "cheat". They leave off the "all channels driven" and quantum only 1 channel at a time which often leads to a higher number. I've seen head units saying "30×4″ which is meaningless but most citizen understand it to mean that the head unit produces 30watts each into 4 channels. That's 120 watts from a head unit. No amp is 100% productive so let us say it draws 150 watts to do this (80% efficiency which is still high). With a 12V power input, the head unit amp's power furnish would be drawing 12.5 amps. I can make sure for you that it is not easy to make a power furnish that fits into a head unit and still leaves enough room for other things for any inexpensive price that can yield that kind of power. That is the conjecture why I say not preferable to use the head unit's power.
Be just with unfinished specs. Even good manufacturers put out incomplete specs and then it is up to you to outline out if the amp is made well or not. Look at the construction and "feel" of the amp as well to make your decision more easy. Also, keep in mind that these explanations are valid for home amplification equipment as well, although the Ftc has more stringent requirements for power claims of home audio equipment.
Amplifier Power Ratings
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