## Destinyyyy one year ago Help with rational exponents and Find all the real and complex roots..

1. anonymous

OKAY

2. anonymous

4x ^3/2 -12=0

3. anonymous

|dw:1440790217001:dw|

4. anonymous

MAKE SURE YOU ISOLATE THE TERM WITH X THEN USE LOG

5. freckles

don't think you need log

6. anonymous

THEN WE DO NOT, LN

7. anonymous

4x ^3/2 =12 x^3/2 = 3

8. anonymous

I have no clue what log is

9. freckles

raise both sides to (2/3) power

10. anonymous

OH i THOUGHT THAT WAS X IN THE EXPONENT HAHA MY BAD

11. anonymous

x= 3 correct?

12. freckles

$x^{\frac{3}{2}}=3 \\ x^{\frac{3}{2} \cdot \frac{2}{3}}=3^{\frac{2}{3}}$

13. anonymous

14. anonymous

Yeah.. Then the x is alone. And 3 *3=9 divide that by 3 = 3

15. anonymous

nooooo lol not like that

16. anonymous

Then what?

17. anonymous

rewrite it as cube root of 9

18. anonymous

As in 9*9*9 ?

19. freckles

no cube root and cube are different terms

20. anonymous

21. anonymous
22. anonymous

So confused

23. freckles

cube of 9 is 9*9*9 but cube root of 9 means $\sqrt[3]{9}$

24. anonymous

25. anonymous

26. anonymous

I have 3^ square root 9 written down already... Whats the next step?

27. freckles

$x^{\frac{3}{2}}=3 \\ x^{\frac{3}{2} \cdot \frac{2}{3}}=3^{\frac{2}{3}} \\ x^{1}=3^\frac{2}{3} \\ x=3^{\frac{2}{3}} \\ x=(3^2)^\frac{1}{3}$ this is how he got cube root of 9 @Destinyyyy

28. freckles

nothing else really to do

29. anonymous

Yes I know that.. Thats the final part? I thought there was more?

30. anonymous

So the answer is -- 3^ square root 9

31. freckles

no not $3^{\sqrt{9}}$

32. freckles

cube root of 9 means $\sqrt[3]{9}$

33. anonymous

Thats no what I mean

34. anonymous

Yeah thats what im saying the 3 up top and square root 9

35. freckles

$x^\frac{b}{a}=\sqrt[a]{x^{b}}$

36. anonymous

37. freckles

you can not do anything with the answer other than what we have already done

38. freckles

unless you are allowed to approximate

39. anonymous

Okay

40. anonymous

(x-3)^ 2/3 =25

41. anonymous

x-3= 25 ^3/2

42. anonymous

Since the 25 is now square root 25 do I change it to 5 and then times it by 3?

43. freckles

you mean write it as 5^3 ?

44. freckles

5^3 is not the same as 5(3)

45. anonymous

I know.. Im saying 5*5*5

46. freckles

$x-3=25^\frac{3}{2} \\ x-3=(25^\frac{1}{2})^3 \\ x-3=5^3$

47. freckles

yes that's right then

48. anonymous

x-3= 125

49. anonymous

So I ignore the 2??

50. freckles

what 2?

51. anonymous

from 3/2

52. freckles

you did the square of 25 already you already used the 1/2 part

53. freckles

then you were left with 5^3 which is 5*5*5 which is 125

54. anonymous

Ohhh... So x= 128

55. freckles

yeah you did it! :)

56. anonymous

Okay :) Find all the real and complex roots. x^4 -12x^2 +27 =0