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

1. anonymous

OKAY

2. Destinyyyy

4x ^3/2 -12=0

3. Destinyyyy

|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. Destinyyyy

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

8. Destinyyyy

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. Destinyyyy

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. Destinyyyy

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

15. anonymous

nooooo lol not like that

16. Destinyyyy

Then what?

17. anonymous

rewrite it as cube root of 9

18. Destinyyyy

As in 9*9*9 ?

19. freckles

no cube root and cube are different terms

20. anonymous

21. anonymous
22. Destinyyyy

So confused

23. freckles

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

24. Destinyyyy

25. anonymous

26. Destinyyyy

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. Destinyyyy

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

30. Destinyyyy

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. Destinyyyy

Thats no what I mean

34. Destinyyyy

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

35. freckles

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

36. Destinyyyy

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. Destinyyyy

Okay

40. Destinyyyy

(x-3)^ 2/3 =25

41. Destinyyyy

x-3= 25 ^3/2

42. Destinyyyy

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. Destinyyyy

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. Destinyyyy

x-3= 125

49. Destinyyyy

So I ignore the 2??

50. freckles

what 2?

51. Destinyyyy

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. Destinyyyy

Ohhh... So x= 128

55. freckles

yeah you did it! :)

56. Destinyyyy

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