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### Course: Arithmetic > Unit 17

Lesson 5: Intro to exponents# 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:

The small number written above and to the right of a number is called an ${\text{exponent}}$ . The number underneath the exponent is called the ${\text{base}}$ . In this example, the base is ${4}$ , and the exponent is ${3}$ .

Here's an example where the base is ${7}$ , and the exponent is ${5}$ :

An exponent tells us to multiply the base by itself that number of times. In our example, ${{4}}^{{3}}$ tells us to multiply the base of ${4}$ by itself ${3}$ times:

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:

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:

That's really long to write. My hands hurt just from typing it! Instead we can see that ${2}$ is multiplied by itself ${6}$ times. This means we can write the same thing with ${2}$ as the base and ${6}$ as the exponent:

Cool, lets make sure we understand exponents by trying some practice problems.

## Practice set:

## Challenge set:

## Want to join the conversation?

- is there a easier way of doing a very long exponents ?(95 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.(221 votes)

- how do I express 144 in exponential form?(28 votes)
- 12^2 is the same as 12 * 12, or 144.(59 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(16 votes)
- for me you hold shift and press 6 so it would be 4^3(17 votes)

- why do we use exponents?(12 votes)
- Hey Aaron, exponents are just a faster (and easier) way to show repeated multiplication.(46 votes)

- how are you supposed to write an exponent when your keyboard doesn't do that(12 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.(27 votes)

- what is 1000000 to the 3rd power? How do u figure out those big type of exponent questions if you get them(10 votes)
- with a calculator(5 votes)

- How do you find out what 4x4x4 is becus3e i got 48 but it says 64(7 votes)
- first you do 4 times 4 which is 16 then 16 times 4 which is 64(12 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.(12 votes)
- Think about it this way; when you subtract a power, you divide by the base the number is. For example 4 to the power 1 is equal to 4 and divide by for again you get 4 to the power 0 which is 1, and 1 to the power 0 is 1/4. Does that make more sense? Your teacher probably was not correct and made a mistake.(2 votes)

- what is 5 to the third power(7 votes)
- 125 because 5x5 is 25 the 5x25 is 125 so 5 to the third power is 125(2 votes)

- hi I experience a lot of this its hard but don ´ t give up!(9 votes)