# Big Powers

##### Age 11 to 16

Challenge Level

What determines whether a number is divisible by $5$ or not?

Find: $3^{1}, 3^{2}, 3^{3}, 3^{4}, 3^{5}, 3^{6}, 3^{7}, 3^{8},
3^{9} \ldots$

What do you notice?

Find: $4^{1}, 4^{2}, 4^{3}, 4^{4}, 4^{5}, 4^{6}, 4^{7}, 4^{8},
4^{9} \ldots$

What do you notice?