The representation of 8 as 2^3 is simply a feature of prime factorization.  Prime factorization is a good practice because it helps identify common terms in the numerator and denominator of any fraction and therefore ensures that cancellations are properly recognized.

For example, when working with fractions it is obviously apparent that the "sevens" in both the numerator and denominator may be cancelled while it may be less obvious that "91/28" has any cancellations at all. After expressing 91/28 in its prime-factored version, (7 * 13) / (2*2 * 7), there is an obvious cancellation.