The student will learn the quotient of powers property of exponents in an authentic context. Division Properties of Exponents (continued).Here you will learn about exponents, division and multiplication of polynomials as well as addition and subtraction of rational expressions. • If the greater base is in the denominator, write the base in the denominator. Then subtract the smaller exponent from the greater. How do I deal with coefficients in the numerator and denominator? Treat the coefficients as separate factors. This property states that when dividing two powers with the same base, we subtract the 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. This property states that when dividing two powers with the same base, we subtract the exponents.