It's not clear what the question means. When we get the 'same thing' each time, is that the thing with the probability of 0.4? Then we just have a sequence of events where we want a certain result each time, so we multiply the probability for each event: the answer would be (0.4)(0.4)(0.4)(0.4) = (0.4)^4.

The question could be interpreted in a different way however. Say you have a slightly weighted coin, and the probability it comes up Heads is 0.4 each time. If I ask "what is the probability you get the same thing each time if you flip the coin 4 times", then there are two ways to get the 'same thing each time': we can get 4 Heads, or we can get 4 Tails. The probability of getting 4 Heads is (0.4)^4. Since the probability of getting Tails on one flip is 1 - 0.4 = 0.6, the probability you get Tails on all 4 flips is (0.6)^4. Since we have two distinct cases, we add the probability from each, and the answer would be (0.4)^4 + (0.6)^4,

Notice we didn't need any formulas here. I've only used the standard 'and rule' and 'or rule' from basic probability. Binomial probability was mentioned in a post above; technically binomial probability questions do occasionally show up at the high level of the GMAT, but you don't need to know what 'binomial probability' even is to answer them, and if you understand the fundamental principles of counting and probability well, you don't need to learn any formulas for them either, though I suppose you could. It's certainly not a topic you should even look at in your studies unless you've mastered nearly everything else, since it is tested so rarely.