I'm going to teach you how to divide exponents that have different bases and where the exponents or powers themselves are also different. In this video, I teach you how to divide exponents (powers) with different bases.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. A. The bases are the same, so subtract the exponents. b. Rewrite the numerator and denominator to show the factors. To simplify expressions with exponents, there are a few properties that may help. Apply properties of operations as strategies to multiply and divide. 2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. The Quotient of Powers Property states that when dividing two exponents with the same base, you can subtract the exponents and keep the base.