So we want to know by which number should we multiply the original amount of the radioactive sample to get the amount that remains after n half-lives pass. If the amount of original radioactive sample is A, then after one half-live there will be (1/2)*A or one half of the amount A. After one more half-life there will be (1/2)*(1/2)*A. After one more half-life there will be (1/2)*(1/2)*(1/2)*A and so on. If we repeat the same procedure n times we get: (1/2)^n*A so the correct answer is C.
