Calculating 5 Cubed

Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

In this lesson, we will discuss what it means to cube a number and go through the step-by-step process of calculating 5 cubed. We will also discuss the basics of exponents and their applications.

Steps to Solving the Problem

So let's say you have five friends who who are each going to pay you five dollars for the next five days. You can figure out how much money you will receive by calculating five cubed or five to the third power. This will tell us how much money you will get because you will multiply 5 by 5 by 5 or 5 cubed.

To start, you need to turn words into numbers by figuring out the base and exponent. An exponent is the number after the ^ which tells you how many times to multiply the base number by itself. The base number comes before the ^. When five is cubed, five is the base number which will show up before the ^.

Three is the exponent and will be the number after the ^. We know three is the exponent because of the word 'cubed,' which always represents the number three.

We can write out five cubed as:


Once the exponent and base are figured out, we need to write out the long version, which shows all the multiplication being done. In this case, the exponent of three tells us to multiply five by itself three times.

5 x 5 x 5

This shows us 5 friends multiplied by $5 multiplied by 5 days.

From here, multiply the numbers out to get the final answer. Multiply two numbers at a time to so you don't make a mistake.

5 x 5 = 25

25 x 5 = 125


The final solution of five cubed is 125. This means you will get $125 from your friends!

Checking Your Work and Application

You want to make sure your friends don't pull a fast one on you so it's important to be sure how much money they owe you. The best way to check your work when using exponents is by working backwards. In order to work backwards, we need to use roots.

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