## anonymous one year ago Rewrite in simplest radical form X^5/6 over x^1/6 Show each step of your process.

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1. anonymous

@lizz123

2. lizz123

@Ashleyisakitty

3. lizz123

@jim_thompson5910

4. anonymous

@KEYS

5. jim_thompson5910

|dw:1434411658371:dw|

6. jim_thompson5910

|dw:1434411694412:dw|

7. jim_thompson5910

since the bases are the same (both x), we can subtract the exponents (top - bottom) |dw:1434411735859:dw|

8. jim_thompson5910

|dw:1434411774461:dw|

9. jim_thompson5910

I'll let you finish up

10. anonymous

x^4/6

11. anonymous

yes? @jim_thompson5910

12. jim_thompson5910

you can then reduce 4/6 to get what?

13. anonymous

2/3

14. jim_thompson5910

correct |dw:1434412037037:dw|

15. anonymous

But we aren't done right?

16. jim_thompson5910

17. jim_thompson5910

we can't reduce 2/3 any further

18. anonymous

|dw:1434412118662:dw|

19. jim_thompson5910

ah they want you to convert to radical form

20. jim_thompson5910

Rule: $\LARGE x^{m/n} = \sqrt[n]{x^m}$

21. jim_thompson5910

m = 2 n = 3 $\LARGE x^{m/n} = \sqrt[n]{x^m}$ $\LARGE x^{2/3} = \sqrt[3]{x^2}$

22. anonymous

Okay:) Thank-you. Mind if I ask another?

23. jim_thompson5910

24. anonymous

Is the expression x3•x3•x3 equivalent to x3•3•3? Why or why not? Explain your reasoning.

25. jim_thompson5910

what are your thoughts on it

26. anonymous

|dw:1434412295575:dw|

27. anonymous

That was the first equation, if u can read it

28. anonymous

|dw:1434412377772:dw|

29. anonymous

That's the 2nd one.

30. jim_thompson5910

what are your thoughts on this? were you able to get started at all?

31. anonymous

Ok so I don't think they are equal

32. jim_thompson5910

and why is that?

33. anonymous

because one is x^27

34. anonymous

and I don't know about the other.

35. jim_thompson5910

|dw:1434412588940:dw|

36. jim_thompson5910

the first one, you use the rule $\Large x^a*x^b = x^{a+b}$

37. jim_thompson5910

and you can extend out the rule the rule basically says "if the bases are the same, then you add the exponents" |dw:1434412649041:dw|

38. jim_thompson5910

|dw:1434412662937:dw|

39. jim_thompson5910

Or you can replace x with some small number, say x = 2 then compute x^3*x^3*x^3 and x^(3*3*3) to see if they are equal or not

40. anonymous

x^9 for the second equation right?

41. jim_thompson5910

|dw:1434412780279:dw|

42. anonymous

So they aren't equal? Right?

43. jim_thompson5910

yeah first one is x^9 the second is x^27

44. jim_thompson5910

I would also use numbers in place of x to test too

45. anonymous

Ok! That's a good idea!! :)

46. anonymous

I have two more questions, and I'm done. Please?

47. jim_thompson5910

I'll help with one more

48. anonymous

Thank you:)

49. anonymous

Which of the following expressions are equivalent? Justify your reasoning. A. 4√x3 B. 1/ x−1 C. 10√x^5•x^4•x^2 D. x^1/3 times x^1/3 times x^1/3

50. anonymous

@jim_thompson5910

51. jim_thompson5910

can you draw out answer C? it's hard to tell where the root ends

52. anonymous

It's over the whole thing, except the 10

53. jim_thompson5910

so it is $\Large 10\sqrt{x^5*x^4*x^3}$ ???

54. anonymous

Yes

55. jim_thompson5910

what does $\Large x^5*x^4*x^3$ simplify to?

56. anonymous

x^11

57. jim_thompson5910

close

58. jim_thompson5910

oh wait I have the wrong digit

59. jim_thompson5910

it should be $\Large 10\sqrt{x^5*x^4*x^2}$

60. jim_thompson5910

so yeah, 11

61. jim_thompson5910

ok I see the answer now

62. jim_thompson5910

what does x^1/3 times x^1/3 times x^1/3 simplify to?

63. anonymous

x^3/3

64. jim_thompson5910

the 3/3 turns into 1/1 or just 1 x^1 = x

65. jim_thompson5910

so in the end, x^1/3 times x^1/3 times x^1/3 turns into just x

66. jim_thompson5910

does choice B say this $\Large \frac{1}{x^{-1}}$ ??

67. anonymous

yes

68. jim_thompson5910

so, $\Large \frac{1}{x^{-1}} = \frac{1}{1/x} = \frac{x}{1} = x$

69. anonymous

Ok

70. anonymous

so, b and d basically

71. jim_thompson5910

yes

72. anonymous

Thank-you so much for all your help:)

73. jim_thompson5910

yw