You can't use Nomex or Romex or whatever we have these days Rick. It's not designed to flex that much or that many times. You would have to install an outlet in the wall behind and then run stranded extension cord type wire to a box in the back of the drawer. And to be up to code it would have to a GFCI plug or GFI breaker in the panel.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.