The source http://imgur.com/DrEinPB states the problem using "256" not "2^8". I'm not sure if the tweeter is trying to be clever, but he isn't saving any characters by using the exponential notation.
If you're trying to save characters in a tweet, you don't have any savings in using exponential over decimal for base two until 2^14.
If you're trying to save characters in a tweet, you don't have any savings in using exponential over decimal for base two until 2^14.