harry_ said:
All of that can be stuffed into a module matching the form factor of a battery. Under 5 amps is generally considered 'low current' and could be done via solid state electronics.
The power stated for the corded Carvex is 500 Watts. To get that much out of a 14.4 V battery would draw a current of almost 35 Amps ( full power ).
To make a transformer/power converter being able to supply that current within the size of the battery pack and with decent bullet-proof cooling, would be quite a challenge given the state of technology. It would certainly move the machine far out of the "affordable, be it only just" range, even if it was possible to engineer at the moment.
Perhaps some kind of hybrid technology using supercaps as a temporary buffer for high current bursts would be a solution, but then again: we expect full power from a corded tool, with full duty-cycle.
It may not be as easy as you think, just my usual 2 eurocents.
Regards,
Job