There is current interest in the possibility that symmetric irradiation of a small pellet of fissionable material by intense laser beams may produce sufficient compression to cause the pellet to become supercritical and thus produce a fission microexplosion. It has been proposed that a repetitive series of such explosions in a suitable chamber could be the basis for an alternative means of generating commercial power from nuclear energy. We present an analysis of this scheme that shows that the energetics do not appear favorable for power generation purposes. Although an input of several hundred megajoules of radiation energy is necessary to trigger a microexplosion, the idea appears to be an interesting physics experiment. Such microexplosions would be unique short-duration sources of nuclear radiations.