Extend the properties of exponents to rational exponents. 1. For this video we are going to look at the division properties of exponents and what we need to remember is what is anything.What Are the Five Main Exponent Properties? This document provides examples and explanations for simplifying expressions involving powers and scientific notation. Topic Overview: Be able to use the properties of exponents. (More properties are introduced in Pre-Algebra.) A quantity with an exponent has three components--the base, the exponent, and the coefficient. Adding and Subtracting Quantities with Exponents. The properties of exponents summarize the structure and patterns that are inherent in exponential expressions. In other words, integers are numbers not written as fractions.