two things, how should i show a prime p, divides a ex.
(p=2^e1 *3^e2 *5^e3....) = a*q?, q is an integer

And why do i need to show that it is less than or equal to the number of times p divides b?

Let's do the second one first. The only way a can divide b is if the number of times every prime p divides a is less or equal to the number of times p divides b. Think about the prime factorization of b/a. Don't you agree?

Let's do the second one first. The only way a can divide b is if the number of times every prime p divides a is less or equal to the number of times p divides b. Think about the prime factorization of b/a. Don't you agree?

No, I'm asking you to compare the number of times p divides a^3 versus the number of times p divides b^2. The first must be less than or equal to the second, right? What does that tell you about ka and kb?