Ahh, I didn't realize you were planning on using a battery. In that case you would only need enough power to keep it charged.
If you were planning on running it from AC only that is were it gets expensive. A Hammond transformer capable of supplying 12V @ 25A runs about $71 from Allied Electronics. This would come close to allowing the amp to reach full power. Add in the cost of some good rectifiers and filter caps and the power supply cost will easily excede the cost of the amp. Of course this is true in many amplifiers, the power supply is often the most expensive part.
The reason you need such a high current power supply is because the voltage is so low. The amp actually has a DC-DC voltage converter inside to raise the voltage up to a level high enough to produce the rated output power. You need approximately 35 volts at the speaker with an 8 ohm load to reach 150watts (35V and 8R works out to 153Watts). If the amp is 90% efficent one would need about 39Volts on the rails to produce this output. Approximatly 4.4 amps will be required at this voltage as well.
Of course since the battery (or supply voltage) is 13.2V this has to be increased. To raise the voltage means transforming current into voltage as nothing is free. Hence if you wanted 5A and 40V you would need 15A of current at 13.2V - and that is just for one channel. Big transformers are not cheap. You could probably get by with a switching power supply but that's not usually in the realm of DIY.
Does this make sense? The numbers are approximate but fairly close.
You could run it off of the 7Ah battery, but at full power (which you won't likely hit very often) it would last about 15 minutes. 7Ah means 7 amps for 1 hour. At 30 amps that is a bit less than 15 minutes. Of course it will last longer at lower power levels. Using a lead acid battery inside is not a very good idea because of the hydrogen gas produced. Don't want your house to go up like the Hindenberg.

A sealed gel-cell is fine though.
Mike