We know that a half-life is the time taken for the activity of a radioactive sample to be reduced to half.
After one half-life, the activity is 1/2 times the original = (1/2)¹
After two half-lives, the activity is 1/4 times the original = (1/2)²
After three half-lives, the activity is 1/8 times the original = (1/2)³
Therefore, the remaining amount of a sample after n half-lives is (1/2)ⁿ
