adi_800 wrote:If (3 ^4 )(5 ^ 6 )(7 ^ 3 ) = (35 ^ n )( x ), where x and n are both positive integers, how many different possible values of n are there?
A. 1
B. 2
C. 3
D. 4
E. 6
OA is C
Wow, lots of discussion about this problem!
3^4 * 5^6 * 7^3 = 5^n * 7^n * x
Since x and n must be positive integers, we can't have more factors of 7 on the right side of the equation than we have on the left side, so largest value of n=3. Since n>0, n = 1, 2, 3.
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