Just to add a note as I was searching for the info and could not find anyone who had posted details.
I have not pulled the extreme apart.. yet.
So I am unsure exactly what value the capacitors are in the onboard power supply.. I have worked extensively on the Time Capsule.. but they are quite a different arrangement.
Testing with a Gen5 Airport Extreme.
I powered it from 9v supply.. worked fine.. 7W power consumption in wireless extender mode with no ethernet connected.
12v is 6.8W
15v is 7.7W
I did not go above 15v as the power consumption was going up, which suggests things are getting hotter. If you have a 15v or 16v laptop supply that should be fine.. do not use unregulated supply that gives voltage above that until I have a chance to inspect the board.
I would have no problems running it on a car battery but would use at least a diode as a protector.
I have long used Time Capsule on SLA battery.