Lucy Lane: All you need is a couple of streaks and your ears pierced. I could do it for you, it's easy. You just get a needle, heat it up, dab it with some alcohol, and zap! The guys go crazy.
Linda Lee: My ears what?
Lucy Lane: Pierced. Like and you know, I take a needle, and then I heat it up, dab it with some alcohol and, zap, all the guys go crazy.
Linda Lee: Because I have holes in my ears?
Lucy Lane: What, are you putting me on? Sometimes I can't figure you out, Linda.
Selena: I'm considering nothing less than world domination.
Lucy Lane: Look at that dingleberry.
Linda Lee: What's a dingleberry?
Nigel: Oh, terrific. The old dangling-in-a-cage routine. Pathetic, Selena.
Answer: The Omegaahedron is the power source for the whole city. It supplies the air, the dome that protects them, the lights, and the machines they need to survive.
The question was why would Zoltar need permission to use the Omegahedron, not what it could do.