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# Intro to exponents

Learn how to use exponents and bases. For example, writing 4 x 4 x 4 x 4 x 4 with an exponent.
Here's what an exponent and a base look like:
start color #11accd, 4, end color #11accd, start superscript, start color #e07d10, 3, end color #e07d10, end superscript
The small number written above and to the right of a number is called an start color #e07d10, start text, e, x, p, o, n, e, n, t, end text, end color #e07d10. The number underneath the exponent is called the start color #11accd, start text, b, a, s, e, end text, end color #11accd. In this example, the base is start color #11accd, 4, end color #11accd, and the exponent is start color #e07d10, 3, end color #e07d10.
Here's an example where the base is start color #11accd, 7, end color #11accd, and the exponent is start color #e07d10, 5, end color #e07d10:
start color #11accd, 7, end color #11accd, start superscript, start color #e07d10, 5, end color #e07d10, end superscript
An exponent tells us to multiply the base by itself that number of times. In our example, start color #11accd, 4, end color #11accd, start superscript, start color #e07d10, 3, end color #e07d10, end superscript tells us to multiply the base of start color #11accd, 4, end color #11accd by itself start color #e07d10, 3, end color #e07d10 times:
start color #11accd, 4, end color #11accd, start superscript, start color #e07d10, 3, end color #e07d10, end superscript, equals, start color #11accd, 4, end color #11accd, times, start color #11accd, 4, end color #11accd, times, start color #11accd, 4, end color #11accd
Once we write out the multiplication problem, we can easily evaluate the expression. Let's do this for the example we've been working with:
start color #11accd, 4, end color #11accd, start superscript, start color #e07d10, 3, end color #e07d10, end superscript, equals, start color #11accd, 4, end color #11accd, times, start color #11accd, 4, end color #11accd, times, start color #11accd, 4, end color #11accd
empty space, equals, 16, times, 4
empty space, equals, 64
The main reason we use exponents is because it's a shorter way to write out big numbers. For example, let's say we want to express the following:
start color #11accd, 2, end color #11accd, times, start color #11accd, 2, end color #11accd, times, start color #11accd, 2, end color #11accd, times, start color #11accd, 2, end color #11accd, times, start color #11accd, 2, end color #11accd, times, start color #11accd, 2, end color #11accd
That's really long to write. My hands hurt just from typing it! Instead we can see that start color #11accd, 2, end color #11accd is multiplied by itself start color #e07d10, 6, end color #e07d10 times. This means we can write the same thing with start color #11accd, 2, end color #11accd as the base and start color #e07d10, 6, end color #e07d10 as the exponent:
start color #11accd, 2, end color #11accd, times, start color #11accd, 2, end color #11accd, times, start color #11accd, 2, end color #11accd, times, start color #11accd, 2, end color #11accd, times, start color #11accd, 2, end color #11accd, times, start color #11accd, 2, end color #11accd, equals, start color #11accd, 2, end color #11accd, start superscript, start color #e07d10, 6, end color #e07d10, end superscript
Cool, lets make sure we understand exponents by trying some practice problems.

## Practice set:

Problem 1A
Write 7, times, 7, times, 7 using an exponent.

## Challenge set:

Problem 2A
Complete the inequality with is greater than, comma, is less than, comma or equals.
2, start superscript, 5, end superscript
5, squared

## Want to join the conversation?

• is there a easier way of doing a very long exponents ?
(56 votes)
• You can use the associative property of multiplication to group numbers.
For example:
3^6 = 3 x 3 x 3 x 3 x 3 x 3
If you do in one at a time: 3 x 3 = 9; 9 x 3 = 27; 27 x 3 = 81; 81 x 3 = 243; 243 x 3 = 729
Using grouping: (3 x 3) x (3 x 3) x (3 x 3) = 9 x 9 x 9 = 81 x 9 = 729

Hope this helps.
(77 votes)
• how do I express 144 in exponential form?
(21 votes)
• 12^2 is the same as 12 * 12, or 144.
(43 votes)
• im wrighting notes on my laptop but i cant figure out how to right it as 4 to the 3rd power with out completely typing a sentence out every time i use open office its the same thing basically as microsoft office
(12 votes)
• that a at great idea
(9 votes)
• why do we use exponents?
(13 votes)
• Hey Aaron, exponents are just a faster (and easier) way to show repeated multiplication.
(34 votes)
• why does math exist
(14 votes)
• It's used as counting money in banks, construction to find coordinates, and many other jobs. It's also not only used in jobs. It's also used in every day things and also math is one of the most important subjects.
(1 vote)
• how are you supposed to write an exponent when your keyboard doesn't do that
(9 votes)
• Use the carat symbol "^" (shift-6) on your keyboard.
For example: 5^3 is understood to be 5 to the power of 3.
Hope this helps.
(7 votes)
• it doesnt show it as correct when i type 1 when the exponent is 0 even though my teacher taught us that it will always be 1.
(10 votes)
• what is 1000000 to the 3rd power? How do u figure out those big type of exponent questions if you get them
(5 votes)
• 1000000000000000000
(5 votes)
• what is 5 to the third power
(6 votes)
• Thank you it did help @ks0607
(8 votes)