The Quotient of Powers Property states that when dividing two exponents with the same base, you can subtract the exponents and keep the base. For this video we are going to look at the division properties of exponents and what we need to remember is what is anything.Know and apply the properties of integer exponents to generate equivalent numerical expressions. To divide exponents (or powers) with the same base, subtract the exponents. Division is the opposite of multiplication. This 2-pack set of notes has been designed to help students practice each exponent rule in isolation, as well as have a mixed set of practice problems. To simplify expressions with exponents, there are a few properties that may help. When dividing exponents, if the bases are the same, you can simply subtract the exponents from the numerator and the denominator.