GMATPrep - exponents again

[allenkt]

I was able to solve this one just by plugging in numbers until I got a combination that worked but I'm wondering if there is an easier way.

[envyk10]

I guess splitting 288 into its factors would help and since you are looking for powers of 2 and 3 => 288 = (2^5)X(3^2)

Therefore, 2^x-1 = 16 & 3^y-2 = 1

Ans 16

[bww]

that's right. with these types of questions, you always want to break down the number into its prime factors. in this case, 2^5 and 3^2 (from 2X2X2X2X2X3X3).

[Cybermusings]

2^5 * 3^2 = 288
Hence x = 5 and y = 2
So 2^x-1 = 2^4
and 2^y-2 = 2^0 = 1
So answer becomes 2^4 * 1 = 16

[chitoshia]

z^(m-n) = (z^m)/(z^n)

That means

288/(2X3^2)

=16

Hence A