prep question

Actually, cybermusings is right.

What is the smallest positive integer n for which 324 is a factor of 6^n?

If n = 2, then we'd be talking about 6^2 = 36. 324 is not a factor of 36.
If n = 4, then 6^4 = 324. 324 is a factor of 324.

Let me just clarify something at the end of cybermusing's explanation:

6^1 = (2^1)*(3^1) allows us to split 6 into its primes

6^n = (2^n)*(3^n) showing the split

324 = (2^2)*(3^4) showing 324 split into its primes

Notice that n (the same number) applies to the exponents for BOTH of the terms, so I cannot just use 324's prime split (2^2 * 3^4). So my two choices are either:

(2^2)*(3^2) OR (2^4)*(3^4)

The first one is too small, so it has to be the second one (n=4).

Also, as a reality check, ALWAYS be wary of choosing the smallest given answer choice on a question that asks for the smallest number or the largest given answer choice on a question that asks for the largest number. Those answers are traps (because a decent number of people will pick those answers simply because they are the smallest / largest numbers presented).