Can somebody explain this physics question on radioactivity please?

Well, 84 days is clearly 10 half-lives for Iodine-131, so the amount of iodine there would have halved 10 times. So to find the fraction of the original amount remaining, we multiply it by 1/2 ten times (ie, by (1/2)^10) to get the final answer of 1/1024 of the original amount.