Well, as long as you are standing on your two feet, the core will always be working. Makes sure to keep the core tight in all your lifts, to effectively transfer energy to the weights. The same goes for jumping, running etc. Elite athletes talk about stiffening their core and compare it to a steel rod (no bend).

Belly dancers, funny enough, generally have alot of problem with their back, because of how much they have to move and flick their spines.