The Rule in Letters

Every product of same-base powers you have combined follows one sentence: a^m * a^n = a^(m+n). The letters make the rule portable: a is any base, m and n are any exponents, and the equation says the counts of factors pool together, whatever they are.

Written in letters, the rule can be checked against its reason: a^m is m factors of a, a^n is n more, and lining them up gives m + n factors. The letters are not new mathematics; they are the same counting argument said once for all cases.

Rules in this general form are worth recognizing on sight, because the rest of the section states each law this way, and because from here on you will use the laws on expressions where the exponents themselves are letters.