Exponentials and Whole Numbers

Background

Let's explore the concept of exponentials some more using whole numbers.

Question

Evaluate:

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Answer

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Analysis

Question 1



Notice that we have two bases - the 3 and the 5. We can't combine them. So all we can do is evaluate the exponentials and then do the multiplication:





(to work the exponential on a calculator, use the  key):





Therefore



Question 2



With this question, we once again have two different bases, 9 and 3. However, remember that  and so we can rewrite our problem:



We can now combine the bases:







Therefore



Question 3

Let's do that same problem we did in 2, but this time do division and not multiplication:



We already know that this equals:



When we multiply bases together, we add the exponents. And so when we divide bases, we subtract bases:



To show how this works, we can expand out the question using 3s:



Or we can simply evaluate it this way:



Vocabulary used:

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

Where might you have come from?

Fact-orials Index

Numbers:

• Whole Numbers

Operations:

• Exponentials

Where might we go?

Operations with different kinds of numbers:

• Exponentials and Whole Numbers - Practice Problems
• Exponentials and Integers