When dividing exponents you're going to subtract the exponents. Can we prepare students for really hairy exponent problems without resorting to memorized rules?For this video we are going to look at the division properties of exponents and what we need to remember is what is anything. To simplify expressions with exponents, there are a few properties that may help. The Quotient of Powers Property states that when dividing two exponents with the same base, you can subtract the exponents and keep the base. In this section, we will define the Negative Exponent Rule and the Zero Exponent Rule and look at a couple of examples. Cluster: Extend the properties of exponents to rational exponents. Standards. Clarifications. Laurie Law, Susan Sabett, Jerry Solinas. National Security Agency Office of Information Security Research and Technology.