Chapter 3. Sets, Exponents, Roots, and Radicals

This chapter explores the concept of sets and how you can use them to help organize groups of numbers. Among key concepts in this respect are unions, intersections, and subsets. Additionally, you can have disjunctions. One approach to illustrating sets involves Venn diagrams, which allow you to visualize relationships between sets. After investigating sets, you then move on to exponents. When you work with exponents, you can perform multiplication operations that involve the same base values by adding the exponents. Likewise, you can perform division operations by subtracting the exponents. After exploring the preliminaries of exponents, you investigate scientific notation, which provides a convenient way to represent microcosmic and macrocosmic values. After exploring scientific notation, you turn to absolute values, which provide a brief introduction to using the number line to represent numbers. As a final measure, you return to exponents, this time to explore how to use radical and root notations in conjunction with exponents. The discussion pursues the following topics, among others:

• How sets and subsets allow you to more easily group numbers

• Basic operations with exponents, including negative values

• How to work with large and small numbers using scientific notation

• Absolute values

• Radical and root notation as an extension of basic exponents