About this video
Sal rewrites 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 as 6 to the eighth power by counting how many 6s are multiplied. He warns that 6^8 is not 6 x 8 = 48; it is a much larger number.
You'll be able to
- write repeated multiplication in exponential notation.
- count the number of factors to find the exponent.
- explain why 6^8 is much bigger than 6 x 8.
Key words
- exponential notation
- A short way to write repeated multiplication, such as 6^8 for eight 6s multiplied together.
- power
- The result of repeated multiplication; '6 to the eighth power' means eight 6s multiplied.
Transcript
Write 6 times 6 times 6 times 6 times 6 times 6 times 6 times 6 in exponential notation. So what's going on over here? Well, we have 6 multiplied by itself how many times? Let's see, that's 6 times 1, then 6 times 2 is that. That's 6 times-- well, it's not 6 times 2.
It's 6 times itself two times. Remember, 6 times itself two times would be 36. 6 times 2 would only be 12. So we have one 6, two 6, three 6, four 6, five 6's, six 6's, seven 6's, eight 6's. So we're multiplying 6 by itself eight times. To write this in exponential notation, we would say that this is equal to 6 to the eighth power, which is literally equal to 6 times 6 times 6 times 6 times 6 times 6 times 6 times 6.
Now, I want to make it very clear this is NOT, this is NOT, this is NOT equal to 6 times 8. 6 times 8 will only be 48. 6 to the eighth power is a super huge number. 6 times 6 is 36, and you're going to multiply that times 6, which is what? That's like 36 times-- that's what?
216, and you keep multiplying it by 6, you get some huge number here. This number right here. It's worthwhile to point out this number is huge. This number right here, not so huge. It is not huge. So don't get confused. If you see 6 to the eighth power, it's 6 times itself eight times, not 6 times 8.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.