Division of Exponents..Please help

Aaring23 wrote:I know this is a pretty basic quesion, but it gave me a little trouble. I was wondering if someone could go through this step by step to show me how to solve.

(8^2)(3^3)(2^4) / 96^2

Answer is 3. Thanks.

We know that we're not expected to solve for 96^2, so there must be a way to cancel things out. So, let's rewrite 96^2 in terms of the numerator.

96 = 8 * 12 = 8 * 2 * 2 * 3

So:

96^2 = (8 * 2 * 2 * 3)^2 = 8^2 * 2^2 * 2^2 * 3^2 = 8^2 * 2^4 * 3^2

Looking at the whole problem:

(8^2)(3^3)(2^4)/(8^2)(2^4)(3^2)

(8^2) on top and bottom - cancel them out
(2^4) on top and bottom - cancel them out
(3^3) on top and (3^2) on bottom. When we divide, we subtract the exponents, so:

(3^3)/(3^2) = 3^(3-2) = 3^1 = 3

Thank a lot. I knew there had to be an easier way. I appreciate the help.

Stuart Kovinsky wrote:
We know that we're not expected to solve for 96^2, so there must be a way to cancel things out.

Aaring,

This is the MOST important step in all of your GMAT prep.

Always focus on what the test-maker is expecting of you. There is no reason for us to do what the test-maker doesnt himself do.

In this case, calculate 96^2

I just factored it as follows:

((2^3)^2)(3^3)(2^4)/(2^5 x 3)^2 =

(2^6)(2^4)(3^3)/(2^10)(3^2) =

(2^10)(3^3)/(2^10)(3^2) =

3^3/3^2 = 3