# CHAPTER 3 - OPERATIONS WITH EXPONENTS AND INTEGERS

### OBJECTIVES

- Identify the types and properties of exponents.
- Perform arithmetic operations with exponents.
- Identify types of roots.
- Perform computations with roots and fractional exponents.
- Perform arithmetic operations with signed numbers.
- Apply rounding rules using significant digits.
- Perform calculations involving scientific notation.

### CHAPTER OUTLINE

3.1 Exponents and Properties (Rules) of Exponents

3.2 Roots, Fractional Exponents, and Negative Exponents

3.3 Arithmetic Operations with Signed Numbers

## Introduction

In Chapters 1 and 2, we learned that **exponents** are used to indicate that a number or expression is to be multiplied by itself a certain number of times. Exponents allow us to perform arithmetic operations more simply than having to use the standard form of a number. A practical application of exponents is used in calculating compound interest on loans and investments. In this chapter, we will expand upon our knowledge of exponents, and look further into the properties of exponents, the relationship between exponents and roots, and how to use exponents to represent extremely large and extremely small numbers through scientific notation.

Furthermore, all of the numbers we have been working with so far have been positive numbers; that is, they lie to the right of zero on the number line. However, every positive whole number, fraction, and decimal number has a negative number known as its opposite, which lies the same distance to the left of zero on the number line. Integers are made up of zero (0), all counting numbers (1, 2, 3, 4, …), and their opposites (–1, –2, –3, –4, …). In this chapter, we will also expand our knowledge of arithmetic operations to include both positively ‘+’ and negatively ‘–’ signed numbers.

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