Some external hard drives come with a single USB cable; they are designed to run on the power supplied by a single cable. Others need a Y cable, with two USB plugs on the PC end, to get enough power.
If your external drive came with just a single USB plug on each end, then the power from that one plug ought to be sufficient, with one big ASSUMPTION: the tablet mini-USB port supplies as much current as does the typical USB port on a PC. I don't know if that's the case.