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Laws of exponents

Exponential notation is a short way of writing the same number multiplied by itself many times. We will now have a closer look at writing numbers using exponential notation. Exponents can also be called indices.

Image

For any real number and natural number , we can write a multiplied by itself times as .

Identity 1

  1. ( because is undefined)

  2. ( because is undefined)

Examples:

Notice that we always write the final answer with positive exponents.

Chapter introduction

Laws of exponents

There are several laws we can use to make working with exponential numbers easier. Some of these laws might have been done in earlier grades, but we list all the laws here for easy reference:

Identity 2

where , and .

Important: when working with exponents, all the laws of operation for algebra apply.

Exercise 1:

Simplify without using a calculator:

1.

 

2.  

 

3.

 

4.

 

5.

 

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7.

 

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