Question

How can you rewrite 9^13 using a root?

Answer 1

You can use a root because a^(1/n) = n√a. For example,

9^13 = (9^26)^(1/2) = √(9^26).

(Indeed (9^26)^(1/2) = 9^(26·1/2) = 9^13.)
Also 9^13 = (9^169)^(1/13) = 13√(9^169), and since 9 = 3^2, 9^13 = 3^26.