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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
• no its not a decimal its just 125 not 41.66666666666666666666
you just used your calculator for that maybe try hand writing it 9 (im not trying to be mean)
• 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!
• 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.
• Noice
• I am struggling with exponents is there any hacks or cheat or even rules to figure these out??
• I need some practice questions per topic. Where do I get them?
• On Khan Academy, there are many practice questions on each subject and you can look them up on Khan Academy at the homepage. Hope that helped!
• what does the symbol ) mean
• i dont understand anything on the video.. can someone help me out please? ! >.<
• Exponents are just repeated multiplication. 5 to power 2 is 5 time itself twice, or 5x5. 5 to power 3 is 5 times itself thrice, or 5x5x5. 5x5=25, and 25x2=125. The value of 5 to power of 3, is 125 or 5x5x5! What else to say!
• so 5 to the 3rd power means to multiply 5*5*5? makes more sense

## 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!