To simplify expressions with exponents, there are a few properties that may help. Here you will learn about exponents, division and multiplication of polynomials as well as addition and subtraction of rational expressions.This property states that when dividing two powers with the same base, we subtract the exponents. The Quotient of Powers Property states that when dividing two exponents with the same base, you can subtract the exponents and keep the base. 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 property which was derived in the previous activity is called the quotient of powers property. O Students complete practice problems on the properties of exponents. Warm Up Simplify. 1. The first law states that to multiply two exponential functions with the same base, we simply add the exponents. There must be two or more variables or constants that are being divided.