## heathernelly 2 years ago awesomeeee.

1. chahnatailor

IS there anything in front of the 3 ?

2. chahnatailor

Or is the question asking the cube root?

3. heathernelly

yeah cube root (:

4. chahnatailor

Ok so, take this step by step. If you have ^3√24a^10b^6 , start with 24 first. Find a perfect cubed number in 24. Do you know what it is ?

5. heathernelly

no :/ im really bad at math:(

6. chahnatailor

A perfect cubed number is anything that has the same 3 numbers multiplied. For example, 3*3*3= 27 so 27 is a perfectly cubed number. If you had the number 54, you would look for factors of 54 that would have a perfect cubed number. So factors of 54 are (1, 2, 3, 6, 9, 18, 27, 54) So if you looked through the numbers, you would see that 27 is the perfect cubed number. So, back to the question, go through the factors of 24 and see what number has 3 of the same numbers multiplied to get that number.

7. heathernelly

3?

8. heathernelly

6, 2, 3, 4, 24, 1, 12, 8?

9. chahnatailor

No... The factors of 24 are (1, 2, 3, 4, 6, 8, 12, 24) .... Now I told you that 3*3*3=27 so it has to be lower. So do 2*2*2 .. That = 8. 8 is a factor of 24 and it is a perfect square.

10. chahnatailor

So, 24 would break into 8 * 3. The 8 will come out of the cube root as 2 ( because 2*2*2=8) leaving you with the 3 in the inside of the cube root.

11. chahnatailor

so you would have 2, ^3√3a^10 b^6 ... get it?

12. heathernelly

wait, why did you chose 8? :/ like how do you know if its a perfect square?

13. heathernelly

ohhh, get it now! your awesome!

14. chahnatailor

Sorry, i meant perfect cube root. What you should do is pull up a list of perfect cube roots. I'll give you the first 10. 13 = 1 23 = 8 33 = 27 43 = 64 53 = 125 63 = 216 73 = 343 83 = 512 93 = 729 103 = 1000

15. heathernelly

thank you soo much :D!!

16. chahnatailor

Ok wait , we're not done!

17. chahnatailor

and the formulas i gave, it is not 13, 23, 33, in the first column. it is supposed to read 1^3, 2^3, 3^3, etc

18. chahnatailor

So now we have to move on to a^10. How many times does 3 go in evenly to 10? (this is because you have ^3√a^10

19. heathernelly

2?

20. chahnatailor

When it comes to exponents for letters, you divide normally instead of trying to find the cube root. Example : ^3√a^7 ... 3 would go into 7 twice so you would have a^6 come out with ^3√a left inside. = a^6, ^3√a

21. chahnatailor

sorry sorry a^2 come out with ^3√a in the inside***

22. chahnatailor

= a^2, ^3√a

23. chahnatailor

So, for ^3√a^10 , how many times does 3 go into 10?

24. heathernelly

that kinda confused me, 3 times r 1? im not sure

25. chahnatailor

3 will go into 10 , 3 times. (3*3 is 9.) .... So a^3 will come out and merge with the 2 from earlier making it 2a^3 and the last a (since only 9 were taken out) will stay inside. So, so far, we have 2a^3 ^3√3a b^6

26. heathernelly

ohh! got you

27. heathernelly

it's actually making more sense now, like as we go on :D!

28. chahnatailor

So, then can you figure out what to do for ^3 √b^6

29. heathernelly

yess, tyy!

30. chahnatailor

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