By going through the method in which we reject a null hypothesis: any observed sample mean value which falls in the rejection region; that is when test statistic > Z(1-alpha) (consider > alternate hypothesis). The definition of Power is the probability of getting an extreme (=alpha) or even more than that. I infer that both refers to the same region and hence their area is nothing different and thus Power is the probability of rejecting a null hypothesis when it is FALSE. Please let me know if I am missing anything. Help much appreciated.
PS: I dont have a statistical background