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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?
• The ^ (or caret) symbol is the exponent symbol, so 1^2 is read one to the second power. I hope that helps!
• 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
• 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)``
• Why do we need exponents?
• Also, when dealing with intergalactic distances we would write 10^14 kms for example otherwise the numbers just eat up a lot of space.
• i dont get how it gets to 125
• 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!
• Noice
• Great explanation
• How do I write the answer?
• 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)
• i don't get this at all
• 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!
• I still don't get it T-T
• 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!