This chapter expands on the material covered in the Powers, Exponents, and Roots section of the SparkNote on Pre-Algebra. Here, we deal with expressions involving both exponents and variables.

The first section reviews the steps for simplifying square roots. In accordance with the convention that fractions should be written without square roots in the denominator, this section also explains how to rationalize the denominator of a fraction--that is, how to eliminate the square root.

The second section builds upon the concept of simplifying square roots. This section explains how to simplify square roots which contain variables.

The next section outlines the properties of exponents--the addition, subtraction, multiplication, division, distribution, and power of a power properties. These properties are used to simplify expressions which contain multiple terms or multiple operations, which is the topic of section four.

Exponents will be important in all the remaining chapters of this study guide. They will be used in scientific notation and they will be part of quadratic and other polynomial equations. Therefore, it is crucial to understand the properties of exponents and to be able to simplify expressions which contain exponents. In order to understand the remaining material in Algebra I and much of the material in Algebra II, one must understand the material covered in this chapter.