? Sure. I even used that knowledge to show off like a dork in a statistics lecture in college. The prof was doing some kind of probability calculation that led to a result of 1 in 4^12, I think, and asked someone to punch 4^12 into a calculator and tell him what it was. Of course, 4^12 is 2^24, which I happened to know by heart was 16,777,216. (Why? It's the number of possible colors on a display that allocates one byte each to the red, green, and blue channels, and it just stuck with me.)
When I rattled off that number a fraction of a second after his asking, without my calculator out, a bunch of folks in the lecture hall turned and looked at me like I was Rain Man or something. Of course, I was just lucky; I couldn't have done it if it hadn't been a reasonably common power of 2.