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. The quotient rule for exponents states that when dividing two numbers with exponents, the exponents can be subtracted when the bases are the same. The Quotient of Powers Property states that when dividing two exponents with the same base, you can subtract the exponents and keep the base. When dividing exponents, if the bases are the same, you can simply subtract the exponents from the numerator and the denominator. This is a fun dance to help you remember PEMDAS. The Wright brothers invented the first practical airplane in the first decade of the twentieth century. Along with this came the rise of aeronautical.