When it comes to their respective departments, the power of a DP is absolute. The camera and lighting crews have one boss, and that boss is the DP. However crazy his ideas seem or whatever harsh demands he has, his crew performs them with what should be minimal complaint.
Outside of his crew, the DP has a hierarchy of folks above him. The director, the producers, studio execs, the union—he's far from autonomous. But still, it's more power than most have on the film set, so make sure you use it to its full capacity: yell things at the grunt workers and demand that someone always be running to get you coffee and snacks.