I would just work with the product of prime factors.

So 96 = 2 x 48
= 2 x 2 x 24
= 2 x 2 x 2 x 12
= 2 x 2 x 2 x 2 x 6
= 2 x 2 x 2 x 2 x 2 x 3 = 2^5 x 3

Obviously its faster if you see that 32 is a factor and 32 = 2^5

Therefore, 96^2 = (2^5 x 3)^2 = 2^10 x 3^2

Is this what you were asking? Is there any sort of question you might want answering?

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

The answer provided is as follows:

(8^2)(3^3)(2^4)
______________

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

= 3

I was hoping to figure how they factored the denominator so easily to eliminate the numerator.

Cheers!

Depending upon the Question you are working, you can apply the method suggested by Moutar: break down the number into its prime factors and then do all the exponential calculations.

However, the Question you provided,
I would advice you not to break 96 into its prime factor

Rather break 96 into factors of 8,3 and 2 because by doing that, you will easily cancel out the terms from Numerator and denominator.

so that saves time for you.

Hope this Helps

Karan