Rocket engine explanation

ok heres the problem. i really need on this. its not a calculation but more of an explanation.

Consider a rocket engine. It delivers a constant thrust, which is the force exerted on the rocket by the expanding exhaust gases from the burning fuel.This typically is true in real life:both the thrust and the rate at which fuel is burned are constant. However, the instantaneous power is given by P=F x v. Since the force is constant, the rocket is accelerating, therefore v is increasing, therefore P is icreasing. However, the fuel is burning at a constant rate; therefore it is producing energy at a constant ratem therefore the power due to the burning fuel is constant. Is there a contradiction here? Explain whats happening, in gory detail.

ok, what i got is the velocity is increasing due to less mass..so less mass the velocity gets faster...what else is needed?