  We consider a natural generalization of the Nagell-Ljunggren equation to the
case where the qth power of an integer y, for q >= 2, has a base-b
representation that consists of a length-l block of digits repeated n times,
where n >= 2. Assuming the abc conjecture of Masser and Oesterl\'e, we
completely characterize those triples (q, n, l) for which there are infinitely
many solutions b. In all cases predicted by the abc conjecture, we are able
(without any assumptions) to prove there are indeed infinitely many solutions.
