newtonian mechanics - If velocity is constant, how can $p = Fcdot v$ be non zero?

If an airplane of mass $m$ is flying at a constant speed $v$, the power of the airplane is

$$P = m\cdot v\cdot g$$ where $g$ is the acceleration of gravity and therefore: $$F = m\cdot g,$$ but, if the velocity is constant, there is no net force as well as no work done. Then how can the magnitude of power be non-zero?