Lesson 1.4

Exponents & Bases

Exponents are a compact way to write repeated multiplication. Understanding the vocabulary of "base" and "exponent" is critical before you tackle the Order of Operations.

Introduction

Instead of writing , mathematicians use exponential notation: . The bottom number is the base and the top number is the exponent (or power).

Past Knowledge

You can multiply whole numbers and recognize repeated addition as multiplication.

Today's Goal

Read and write expressions using exponents. Identify the base and power. Evaluate simple powers.

Future Success

Exponents appear in every algebra course — from PEMDAS to polynomial degrees to exponential growth.

Key Concepts

1. Anatomy of a Power

BaseThe number being multiplied

ExponentHow many times to multiply

2. Reading Powers Aloud

Expression	Read As	Value
	"5 squared"
	"2 cubed"
	"4 to the fifth power"

3. Special Powers

Exponent of 1

Any number to the first power is itself:

Exponent of 0

Any nonzero number to the zero power is 1: (we'll prove this later!)

Worked Examples

Example 1: Evaluate a Power

Basic

Evaluate .

Expand

Multiply Step by Step

Example 2: Write in Exponential Form

Intermediate

Write in exponential form.

Count the Factors

The number appears 5 times.

Write as a Power

Example 3: Negative Base

Advanced

Evaluate and compare with .

: The negative IS the base

: Only 2 is the base

Same answer here — but try with an even exponent and you'll get different signs!

Common Pitfalls

Multiplying Base × Exponent

. The exponent tells you how many times to multiply, not to multiply by it. .

Parentheses with Negatives

but . The parentheses make all the difference!

Real-Life Applications

Computer storage is measured in powers of 2. One kilobyte is bytes, one megabyte is bytes, and one gigabyte is bytes. Every tech company depends on exponents.