Multiplication and Division Properties of Exponents Total Points: 49 Simplify each of the following and show all work. To simplify expressions with exponents, there are a few properties that may help.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. When dividing exponents, if the bases are the same, you can simply subtract the exponents from the numerator and the denominator. 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.