When there is a function notation problem that is, for instance, f(x)=2^x and you have to find for f(x+3), I know that the (x+3) replaces the x in 2^x, but then do you distribute the x and the 3 or do you just leave it as 2^(x+3)?
Good question. The expression you get is 2^(x+3) and that expression answers the question.
If you're going to simplify the expression, which isn't necessary on this question but is on some subsequent questions, you have to use the standard rules of algebra. In this case you need to use the laws of exponents.
Recall that a^(b + c) = a^b * a^c. So
2^(x+3) =
2^x * 2^3 =
2^3 * 2^x =
8 * 2^x.