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?