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.One is that when two numbers with the same base are multiplied, the exponents can be added. 7.1 Exponents click here. 7.3 Multiplication Properties of Exponents click here. The quotient rule for exponents states that when dividing two numbers with exponents, the exponents can be subtracted when the bases are the same. To do this, use the Quotient Property of Exponents, which says that when you. Divide two expressions with the same base, you can subtract the exponents. M. Sovereign Godsent. If the terms have different bases, you cannot combine them.