How do you divide exponents with different powers? If the exponents have the same base you just subtract the exponents.Then, exponents get dealt with (including roots). 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. Mathematics is so much more than memorizing rules. It is learning to reason, to make connections, and to make sense of the world. To simplify expressions with exponents, there are a few properties that may help.