## kandsbbf 2 years ago What is a simpler form of the radical expression?

1. kandsbbf

|dw:1358117374152:dw|

2. kandsbbf

@Butterfly16

3. kandsbbf

some pls help

4. kandsbbf

@loveudrew123

5. nooce

Simplify the x^12 and y^16 first

6. nooce

Remember:$(x^a)^b x^{a• b}$

7. kandsbbf

do i just simplify the exponents?

8. nooce

We're simplifying them first, cause it's easier haha, we'll move on to the 240 after you simplify the exponents

9. nooce

2901*

10. kandsbbf

so how do i simplify them?

11. nooce

Well since, $(x^a)^b = x^{a•b}$ divide x^12 and y^16 by 4. What do you get?

12. nooce

(I mean the powers of x and y)

13. kandsbbf

x^2 x^4

14. nooce

Wait, but 12/4 = 3, not 2. Also, it would be y^4

15. nooce

But moving on, now we simplify $\sqrt[4]{2901}$ Do you have any idea on how to do this? (just asking)

16. kandsbbf

no lol, but i really appreciate u teaching me

17. nooce

No problem, I'm glad to help :) Well, first, we need to find a factor of 2901 that is a power of 4. (ex. 16, because 2^4 = 16)

18. kandsbbf

how do we do that lol

19. nooce

Here's a list of em: $2^4 = 16$ $3^4 = 81$ $4^4 = 256$ $5^4 = 625$ $6^4 = 1296$ Are any of these numbers factors of 2901?

20. kandsbbf

no i get dec. for all of them

21. nooce

The number in the problem is 2901, right?

22. nooce

Or is it 2401?

23. nooce

because, $7^4 = 2401$

24. kandsbbf

2401 sorry(:

25. kandsbbf

@nooce

26. nooce

Alright, since we know 2401 = 7^4, we can take that out of the radical :) So we get, $\sqrt[4]{2401x^{12}y^{16}} = 7x^3y^4$ Do you get it? :D

27. kandsbbf

yes thankyou!