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.To simplify expressions with exponents, there are a few properties that may help. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve. 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 divide powers with the same base, subtract their exponents. A negative exponent can be written as a positive exponent in the denominator. Michigan's K–12 academic standards serve to outline learning expectations for. Michigan's students and are intended to guide local curriculum development. Understand properties of multiplication and the relationship between multiplication and division.