Another question made me remember this.
Consider a sizable base (building, station) in the atmosphere of a gas giant planet. It should hold a staff of a couple hundred, with supplies and scientific instrument for the mission.
One mission it has is to lower things on a loooong cable. I mention this because the tether technology is available to apply to these questions.
how does it stay afloat?
It needs to hover indefinitely. You can't make a boyant balloon in an atmosphere that's already made of the lightest gas. So hot air, or engines, or ride updrafts, or what?
what does it use for power?
Fusion from locally sourced hydrogen would be an easy answer. But suppose that's not available (or not practical); or maybe some other power source is wonderfully elegant if you can think of it?