if i smite a unit while the opponent has zhonyas active, what happens?

It's up to your opponent — they control Zhonya's Hourglass, so they pick the order of the two replacement effects, and if they apply Zhonya's first the unit is saved instead of banished.

Both effects are replacement effects competing for the same death (Rule 373), so the controller of the affected unit's replacement effect orders them. Zhonya's replaces the death with heal/exhaust/recall, which means the "would die" event never happens — and since Smite's banish only replaces a death, it has nothing left to modify. Your Smite's 3 damage still gets dealt; it just doesn't turn into a banish. Note this only works because it's their unit — Zhonya's can only protect a unit its controller controls, so it can't save a unit you own from your own Smite.