Copyright

Solving 5 to the 4th Power

Solving 5 to the 4th Power
Coming up next: Solving 5 to the Negative 4th Power

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:04 Steps to Solve the Problem
  • 1:38 Solution
  • 2:07 Ways to Check Your Answer
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Timeline
Autoplay
Autoplay
Speed
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.

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account
Support