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Exponents with fractions and - sign

  1. Aug 26, 2011 #1
    what does this simplify to: (-33/2)2/3

    I use the exponent rules to multiply the fractions to get (-31) which comes out to -3, but the answer key says the real answer is 3. Is there something important when doing fractional exponent that I'm missing out? Thanks in advance.
  2. jcsd
  3. Aug 26, 2011 #2


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    Staff Emeritus
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    [itex]\left(-3^{3/2}\right)^{2/3}=[/itex][itex] ((-3^{3/2})^2)^{1/3}[/itex]
    Does that clarify it?

    Another way to look at it is that [itex](-3^{3/2})^{2/3}=[/itex][itex](-1)^{2/3}(3^{(3/2)(2/3)})[/itex]. [itex](-1)^{2/3}= 1[/itex], not -1.
    Last edited: Aug 26, 2011
  4. Aug 26, 2011 #3

    Ray Vickson

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    Use of the "rules of exponents" is NOT recommended when you have fractional powers of negative quantities. If you interpret your quantity as A = [(-3)^(3/2)]^(2/3), using the laws of exponents gives A = (-3)^1 = -3. However, the actual value (using general definitions in terms of functions in the complex plane) is A = (3/2) - I*(3/2)*sqrt(3), where I = sqrt(-1). On the other hand, if you meant to write B = [-(3^(3/2)]^(2/3), the laws of exponents gives B = (-1)^(2/3)*3 = (-1)^2*3 = 3. However, the actual value is B = -(3/2) + I*(3/2)*sqrt(3).

  5. Aug 26, 2011 #4


    Staff: Mentor

    I don't believe this is a correct interpretation of the problem. The OP shows it as -33/2, not (-3)3/2.
    This is probably overkill in the context in which this problem was posed (as a prealgebra problem). I believe HallsOfIvy's approach is the right way to go, although it appears that he omitted a factor of 3 towards the end of his calculation.

    Corrected, it would be (−33/2)2/3=(−1)2/3(3(3/2)(2/3)) = 1 * 3 = 3
    Last edited: Aug 26, 2011
  6. Aug 26, 2011 #5
    (−33/2)2/3=((−33/2)2)1/3 That I got but (−33/2)2/3=(−1)2/3(3(3/2)(2/3)). (−1)2/3 . 3 = 3 this i do not get. Why is there a multiplication factor there?

    side note. how do you copy and paste while keeping super and subscripts?
  7. Aug 26, 2011 #6


    Staff: Mentor

    Because -3 = -1 * 3. That's really all that's going on for that part.
    You can't. I had to reproduce the superscripts from what I had copied.
  8. Aug 26, 2011 #7
    (−33/2)2/3=(−1)2/3(3(3/2)(2/3)). (−1)2/3 . 3

    looking at that equation, I understand that -3 is the same thing as -1*3 and so that is where (−1)2/3(3(3/2)(2/3)) came from but the additional (−1)2/3 . 3 after that I don't get. where did that last part come from? is the first . supposed to be a multiplication sign or a period? if it is a period it would make sense.

    is (x-1/3)/(y-1/3)=(y1/3)/(x1/3)
    Last edited: Aug 26, 2011
  9. Aug 26, 2011 #8


    Staff: Mentor

    You're right - it shouldn't be there. I copied from HallsOfIvy's post and didn't notice that extra stuff. I corrected it in my earlier post. The expression in HTML is quite complicated, with all those SUP and /SUP tags, so I can see that it would be easy to forget to put something in, which is what I believe happened. Sorry for adding to the confusion.
    The period is meant to indicate multiplication. I changed it to * to make that clearer.
  10. Aug 26, 2011 #9
    Ah then it is perfectly clear. Thanks for the help.
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