The main difference to air breathing engines is that both your fuel and oxidizer are dense liquids so their volume is a thousand times less than comparable ambi

The main difference to air breathing engines is that both your fuel and oxidizer are dense liquids so their volume is a thousand times less than comparable ambient air (never mind the nitrogen). Still, if you think that's a lot of power, only a few percent of the propellant is burned to run the pumps. Something like 20x burns in the main chamber, the aim being to accelerate the exhaust gases. The power of that jet can be gigawatts, though it's relatively meaningless.