Multipying & Dividing Rules
Product of Powers
How does an expression like 
simplify? Notice that both terms have the same base. When a product of two or more terms has the same base to a power, the exponents can be added.
Product of Powers Rule:xn·xm = xn+m
Why does this rule work? Using the expression above and writing out the expansion of each term creates the following steps:
This rule is a nice "shortcut" for the multiplication of terms, but it only applies to exponents with the same base. Therefore, it will not work for 
, because the bases are not the same.