# Solving 5 to the 4th Power

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• 0:04 Steps to Solve the Problem
• 1:38 Solution
• 2:07 Ways to Check Your Answer
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Lesson Transcript
Instructor: Sharon Linde
What are exponents and how do they work? This lesson explains this process using the example of raising 5 to the 4th power. We'll go over the process step by step.

## Steps to Solve the Problem

What does raising 5 to the 4th power mean? What number do you get at the end of this process?

Exponents are numbers written in a smaller size to the upper right of other numbers or expressions. While exponents are easy to write that way by hand, in some popular software applications and in text editors that don't allow for exponents, it is common to see them written with a caret (^) separating the number and power, like this: 5^4.

Step one is to expand the expression. You might be saying to yourself, 'Never mind how it is shown, what does it mean?' That is an excellent question. 5 raised to the 4th power just means that the number five is multiplied by itself 4 times, like this:

5^4 = 5 * 5 * 5 * 5

Step two is to start multiplying. The associative property of multiplication means that our problem can be solved in a number of different ways. We can choose any two pairs of number in our equation to multiply and replace them with their product. Since we know 5 * 5 = 25, we can change our equation to:

5^4 = 25 * 5 * 5

Step Three is to multiply again. We still have another 5 * 5, so we can multiply and substitute again:

5^4 = 25 * 25

Step four is to multiply one last time. Finally, we can use whatever method we want to get the product of 25 * 25. A calculator, software program, phone, multiplication by hand, or even memorization of perfect squares will all work to get you the answer.

## Solution

Whichever method you choose to solve the last step will give you our answer for 5 raised to the 4th power: 625.

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