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.The quotient rule for exponents states that when dividing two numbers with exponents, the exponents can be subtracted when the bases are the same. What is the correct simplification? 24. Reasoning The division property of exponents says that to simplify powers with the same base you subtract the exponents. When dividing exponents, if the bases are the same, you can simply subtract the exponents from the numerator and the denominator. (H) solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders. (5). Algebraic reasoning.