# Chapter 8: Exponential Functions

**At Grade**Created by: CK-12

## Introduction

In the world of real estate, the size of homes and buildings is measured in “square feet.” What does this terminology mean? One square foot equals 1 foot x 1 foot or \begin{align*}1^2\end{align*} foot. The two in this expression is an exponent and it represents repeated multiplication. The various exponential properties that allow you to combine multiple exponents into a single one are the focus of this chapter. Once you’ve mastered these techniques, you’ll be able to evaluate what at first appear to be complicated exponential expressions.

- 8.1.
## Exponential Properties Involving Products

- 8.2.
## Exponential Terms Raised to an Exponent

- 8.3.
## Exponential Properties Involving Quotients

- 8.4.
## Exponent of a Quotient

- 8.5.
## Negative Exponents

- 8.6.
## Fractional Exponents

- 8.7.
## Evaluating Exponential Expressions

- 8.8.
## Scientific Notation

- 8.9.
## Scientific Notation with a Calculator

- 8.10.
## Geometric Sequences and Exponential Functions

- 8.11.
## Graphs of Exponential Functions

- 8.12.
## Applications of Exponential Functions

### Chapter Summary

## Summary

This chapter begins with four important properties for combining exponents: Product of Powers, Power of a Product, Quotient of Powers, and Power of a Quotient. Negative, zero, and fractional exponents are discussed next. All these properties come together in the evaluation of exponential expressions. A way of representing very large and very small numbers more simply, known as scientific notation, is next covered. The chapter wraps up with discussion of geometric sequences and exponential functions, with an emphasis on real-world applications.