If I choose four cards from a standard -card deck,with replacement, what is the probability that I will end up with four cards from the same suit?

Since there are 4 suits and the number of possible four-card choices from each suit is 13C4, the probability you are looking for is

\(\frac{4(13C4)}{52C4}\)\(=\frac{2860}{270725}\)

A calculator would simplify that for you.