Exponentials and Integers

Background

We know how to handle exponentials with whole numbers but what happens if we put in integers?

Question

Evaluate:

1.  
2.  
3.  
4.  

Answer

1. 
2.  
3.  
4.  

Analysis

Let's work through a question we know before diving into what we don't know:

Question 1

We know that the base is 3 and the exponential is 2, which gives:



Question 2

We know that the base is -3 and the exponential is 2, which gives:



Question 3

Here we have a negative number in the exponential position. What does that mean?

When we have a negative exponential, we put the base into the denominator with the positive exponential. With our current question, that looks like this:



Question 4

We work this the same way as we did above:



General Rule:



Vocabulary used:

• base - in an exponential term, the number that is being multiplied
• exponential - in an exponential term, the number that says the number of times to multiply the base

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Numbers:

• Integers
• Fractions and Decimals

Operations:

• Exponentials

Operations with different kinds of numbers:

• Exponentials and Whole Numbers

Where might we go?

Operations with different kinds of numbers:

• Exponentials and Integers - Practice Problems