If a,b,c are integers all greater than 1, and 15^8 = a * (b)^c. What is the value of c?

1 - a is not divisible by 5
2 - b is not divisible by 3

I will post the OA after some discussion.

My approach

(3)^8 * (5)^8 = a * (b)^c

Statement 1 tells us a cannot have a 5 in its factor.
Statement 2 tells us b cannot have a 3 in its factor.

Since all are greater than 1
By comparing the equations a = 3^8 ; b =5
Hence c = 8.

IMO C