## anonymous 5 years ago 3nth sqrt (x-9)^3

1. anonymous

$(\sqrt[3]{x-9})^3$ If you cube a cubed root you just remove them both. $\sqrt[3]{a^3} = \sqrt[3]{a}^3 = a^{\frac{3}{3}} = a^1 = a$

2. anonymous

its whats inside the radical thats confusing me

3. anonymous

x - 9 is just x - 9

4. anonymous

Or do I misunderstand your question?

5. anonymous

well. i have another problem thats like that and i just dont know what to do with (x-anything)^anything

6. anonymous

Just expand it and simplify as much as possible. Unless you have an equal there you can't really solve for x.

7. anonymous

so you foil within the radical to expand it?

8. anonymous

Well if it's something cubed inside a cubed root, there's no need to foil it cause the two cancel eachother out. Otherwise yeah you'd have to distribute (foil) and hope it turns out nicely.

9. anonymous

so the answer is just x-9

10. anonymous

Yep.

11. anonymous

Assuming that it is as I have it written originally.

12. anonymous

thank you, can you help me with sqrt 25(x+2)^4

13. anonymous

Of course.

14. anonymous

Can you quickly rewrite each of those factors as a square?

15. anonymous

25 is what squared?

16. anonymous

5

17. anonymous

And $$(x+2)^4$$ is what squared?

18. anonymous

that i dont know

19. anonymous

Oh. well what if I asked you what $$(2^2)^2$$ was. Do you know that?

20. anonymous

wouldnt that be 16?

21. anonymous

Yes, but don't think about it that way ;p

22. anonymous

Think about it as $$2^4$$

23. anonymous

When you raise a power to a power you multiply the exponents

24. anonymous

Have you been taught this?

25. anonymous

the teacher i have sucks. so probably have but not the way your explaining it

26. anonymous

Hrm. Ok, well so if raising something to a power multiplies exponents, then taking the root of a power divides the exponent.

27. anonymous

For example. $\sqrt{5^4} = 5^2$ $\sqrt[3]{7^{12}} = 7^4$ etc.

28. anonymous

So if you have $\sqrt{a^4} =\ ?$

29. anonymous

okaie. so would (x+2)^4 would just be x+2 ^ 2. and the answer to your question is a^2

30. anonymous

Yes precisely. So for your problem you had $\sqrt{5^2(x+2)^4} =\ ?$

31. anonymous

well it was 25 which = 5^2.

32. anonymous

Right. Same difference, so take the square root of that and you get?

33. anonymous

5(x+2)^2

34. anonymous

Exactly.

35. anonymous

THANKK YOU SO MUCH<!!!!

36. anonymous

Very welcome ! =)

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