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### Course: Algebra basics > Unit 1

Lesson 3: Exponents- Intro to exponents
- Exponent example 1
- Exponent example 2
- Squaring numbers
- Intro to exponents
- The 0 & 1st power
- Powers of zero
- Meaning of exponents
- 1 and -1 to different powers
- Comparing exponent expressions
- Exponents of decimals
- Powers of whole numbers
- Evaluating exponent expressions with variables
- Variable expressions with exponents
- Exponents review

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# Exponent example 1

Sal explains the difference between 5 × 3 and 5 to the third power. Created by Sal Khan.

## Want to join the conversation?

- what does this symbol ^ mean?(133 votes)
- The ^ (or caret) symbol is the exponent symbol, so 1^2 is read one to the second power. I hope that helps!(227 votes)

- I'm probably jumping way too far ahead but... is there an operation represented by the ? mark below?

5*3 = 5+5+5

5^3 = 5*5*5

5?3 = 5^5^5(61 votes)- I’ll make an example with the base of 2 so it will be easier to compute the values in mind.
`2×2×2 = 8 = 2^3 = 2^1×2^2 = 2^(1+2)`

2^3^2 = 8^2 = 64 = 2^6 = (2^3)^2 = 2^(3×2)

so if the base (2 or 5, in this examples) is defined as “a” and the exponent values (1 and 2; or 3 and 2 in this examples) are defined as “m” and “n”, then we will get:`a^m×a^n = a^(m+n), while`

(a^m)^n = a^(m×n)(0 votes)

- Why do we need exponents?(7 votes)
- Also, when dealing with intergalactic distances we would write 10^14 kms for example otherwise the numbers just eat up a lot of space.(5 votes)

- i dont get how it gets to 125(3 votes)
- So when you time 5 by itself 3 times you get 125

5^3(^ symbol is what we use to symbolize exponents)

5 x 5 x 5 = 5^3

so the first two 5 is 25(5x5=25)

now we have 25 x 5

25 x 5 = (20 + 5) x 5

(20 x 5) + (5x5)

100 + 25

125

Another example: 4^2 = ?

since "^2" says the power is rise to 2 that means we take the left number(4) and multiple it by itself 2 times

4 x 4 = 4^2

Now what is 4 x 4? 16

16 = 4^2

As you see the equation tells us that 4^2 is in fact 16

Try the practice problems on paper so your brain will make the logical connections of the symbols and results!(12 votes)

- Great explanation(5 votes)
- How do I write the answer?(3 votes)
- If you mean you want to write the answer with an exponent then you can do this:

Example: write five to the power of four in number form

Number form: 5^4 (I just put the "^" sign to show 4 is an exponent)(5 votes)

- i don't get this at all(3 votes)
- So when you time 5 by itself 3 times you get 125

5^3(^ symbol is what we use to symbolize exponents)

5 x 5 x 5 = 5^3

so the first two 5 is 25(5x5=25)

now we have 25 x 5

25 x 5 = (20 + 5) x 5

(20 x 5) + (5x5)

100 + 25

125

Another example: 4^2 = ?

since "^2" says the power is rise to 2 that means we take the left number(4) and multiple it by itself 2 times

4 x 4 = 4^2

Now what is 4 x 4? 16

16 = 4^2

As you see the equation tells us that 4^2 is in fact 16

Try the practice problems on paper so your brain will make the logical connections of the symbols and results!(5 votes)

- I still don't get it T-T(4 votes)
- So when you time 5 by itself 3 times you get 125

5^3(^ symbol is what we use to symbolize exponents)

5 x 5 x 5 = 5^3

so the first two 5 is 25(5x5=25)

now we have 25 x 5

25 x 5 = (20 + 5) x 5

(20 x 5) + (5x5)

100 + 25

125

Another example: 4^2 = ?

since "^2" says the power is rise to 2 that means we take the left number(4) and multiple it by itself 2 times

4 x 4 = 4^2

Now what is 4 x 4? 16

16 = 4^2

As you see the equation tells us that 4^2 is in fact 16

Try the practice problems on paper so your brain will make the logical connections of the symbols and results!(2 votes)

- how do you get the whiteboard(4 votes)

## Video transcript

Find the value of 5 to
the third power. Let me rewrite that. We have 5 to the third power. Now, it's important to remember,
this does not mean 5 times 3. This means 5 times itself three
times, so this is equal to 5 times 5 times 5. 5 times 3, just as a bit of a
refresher so you realize the difference, 5 times 3-- let
me write it over here. 5 times 3 is equal to
5 plus 5 plus 5. So when you multiply by 3,
you're adding the number to itself three times. When you take it to the third
power, you're multiplying the number by itself three times. So 5 times 3, you've seen
that before, that's 15. But 5 to the third power, 5
times itself three times, is equal to-- well, 5 times 5 is
25, and then 25 times 5 is 125, so this is equal to 125. And we're done!