# Using Exponents on a Scientific Calculator

Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

In this lesson, we will review what exponents are and how to calculate them. We will then look at how to use exponents on a scientific calculator and look at a couple of examples of doing so.

## Exponents

What do you think of ants? Some would say they're creepy while others admire their work ethic and even think they're a little cute! Let's say that you decide to study these little guys for the next six months, so you make an ant farm. You start with just two ants in your farm, and soon realize that they are increasing in number in such a way that their population doubles each week.

Week Population
1 2
2 4
3 8
4 16
5 32

This pattern continues, and it appears that the population of ants can be found by multiplying 2 by itself the number of weeks that have gone by. For instance, at week three, we find the population by multiplying 2 by itself 3 times.

2 ⋅ 2 ⋅ 2 = 8

At week three, the ant population is 8. We're actually dealing with something called exponents in this example. When we are multiplying an expression, call it a, by itself a number of times, that number is called an exponent. We say that we are raising the expression to the power of the exponent, and we write

ax

where x is the exponent. To put this into perspective, consider your ants again. We said that to find the population of ants, we multiply 2 by itself the number of weeks that have gone by. If we call the number of weeks that have gone by w, then we have that the population is 2w.

We see that the number of weeks, or w, is the exponent, and finding the population after w weeks is simply a matter of raising 2 to the power of w.

## Using Exponents on a Scientific Calculator

It's pretty easy to find the ant population for the first few weeks. However, what if we wanted to know what the population would be after 8 weeks? We would want to find 28, and that would mean multiplying 2 by itself 8 times! I don't know about you, but doing this by hand seems like a tedious job to me. Even if we use a basic calculator, our fingers might get sore from having to push 2 times 2 times 2 times 2, and so on! Thankfully, there's an easier way - the scientific calculator!

A scientific calculator is a calculator that is capable of performing operations that are more advanced than simple addition, subtraction, multiplication, and division, but it does not have graphing capabilities. Thankfully, these types of calculators are able to deal with exponents with a few simple keystrokes.

The exponent button varies on different scientific calculators. It can have a variable raised to a variable, such as xy or ax, or it could be something as simple as a triangle without a bottom side (^).

In the same way that the button's appearances vary from calculator to calculator, the keystrokes that we take to raise x to the power of y also varies from calculator to calculator. It may be that you hit the button x, then hit your exponent button, then hit the button y. Or, you may enter your exponent y first, then your exponent button, then x. It could also be that you hit your exponent button first, then x, then y.

Uh, all these options are kind of making things confusing! Don't worry! Your calculator manual will tell you how to calculate exponents on your calculator. For now, we will just consider the most common keystroke pattern for calculating xy, and that is as follows:

1. Enter the number x.
2. Hit the exponent button.
3. Enter the number y.
4. Hit 'Enter' (or =).

Four buttons, and you've got your answer! Awesome! Let's look at some different ant populations depending on how long you've had your ant farm!

## Examples

We were talking about what the ant population would be at 8 weeks, so we want to find 28. To figure this out, we grab our trusty scientific calculator and plug away! First, we enter the number 2. Next, we hit the exponent button then enter the number 8. Lastly, we hit 'Enter'.

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