I'm going to teach you how to divide exponents that have different bases and where the exponents or powers themselves are also different. To simplify expressions with exponents, there are a few properties that may help.For this video we are going to look at the division properties of exponents and what we need to remember is what is anything. 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. So when you multiply exponents with the same base, you add the exponents. The quotient rule for exponents states that when dividing two numbers with exponents, the exponents can be subtracted when the bases are the same. Under the following conditions: Attribution. In the examples, the bases are varying rational numbers. Use the Properties to Divide Exponents.