This is a proof demonstrating mathematical induction, and relies on a much more basic understanding of exponentials. (no offense meant) You can't add things like that. If two things are multiplied, the exponents add, but not if those two things are added. You might have been able to get the right answer in this case, but it's for the wrong reason- it's because it is base two, and not a generic answer because of that. Exponents are not too hard for you, I happen to know that you are plenty smart, in my experience. My recommendation is to find an algebra text (say, College Algebra) that is for College Freshmen and re-work through the section on handling exponentials. That same text will have the details of proof by induction, possibly with a less complicated example.
If you get to thinking you’re a person of some influence, try ordering somebody else’s dog around.
