Jack has a giant apple pie. On the first day, he eats half of the pie. For each following day, he eats half as much pie as he did the day before. What fraction of the original pie did he eat on the tenth day?

on the first day, he eats half the pie.

the next day, he eats half of half of a pie. this is 1/4 of a pie.

so it is just the powers of 2, starting with 2^1=2.

so on the tenth day, it is 1/(2^10) or 1/1024 of a pie.

HOPE THIS HELPED!

(1/2)^10 = 1/1024 of a pie on the 10th day