The basic rule for dividing exponents with the same base is that we subtract the given powers. This is also known as the Quotient Property of Exponents.For this video we are going to look at the division properties of exponents and what we need to remember is what is anything. These are the forms that Clerk's office provides for Circuit Civil cases. The quotient rule for exponents states that when dividing two numbers with exponents, the exponents can be subtracted when the bases are the same. What is the correct simplification? 24. Reasoning The division property of exponents says that to simplify powers with the same base you subtract the exponents.