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Exponent questions

  1. Aug 2, 2011 #1
    1. The problem statement, all variables and given/known data

    http://i51.tinypic.com/2zyfyaa.jpg

    Question 3 l )



    2. Relevant equations



    3. The attempt at a solution

    (6a^-2b^-3)^2
    (__________) 1/6a^2 * 1/b^3 / 1/2a^2 * 1/b^1
    (2a^2b^-1 )

    I multiplied the top half together to give me 1/ 36a^4b^2

    Multiplied the bottom half to give me 1/4a^4b^1 , Then took the reciprical of the bottom half and move it up and multiplied it with the top half.

    Giving me a final of

    :: 4a^4b^1
    __________
    36^a4b^5

    However, when i fold this down it becomes 1/9 and the a's cancel and 4b is left over at the bottom.

    The answer is a^8b^4 / 9

    I know its complicated to read, just write it on paper and ull understand.

    What did i do wrong?
     
  2. jcsd
  3. Aug 2, 2011 #2
  4. Aug 2, 2011 #3
    Or... f) (-3m^-3n^-1)^-3

    Solving this one, I get -27m^9 / n^3

    Why in the answer book is it m^9*m^3 /27 ?

    Anyone....?
     
  5. Aug 2, 2011 #4

    eumyang

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    You continue to write out your problems in a way that makes it hard to read. I think others would be less willing to help you because of this. Learn LaTeX, for goodness sake!

    In any event, if I am reading your work correctly, this line:
    is wrong. It should be 1/ 36a^4b^6.

    Anyway, your approach is rather confusing. It looks like you want to start by rewriting the negative exponents to positive ones. I wouldn't do that. Instead, divide the numerator by the denominator, subtracting exponents as you go:
    [itex]\left(\frac{6a^{-2}b^{-3}}{2a^2 b^{-1}}\right)^{-2} = \left(3a^{-4}b^{-2} \right)^{-2}[/itex]
    Then "distribute" the -2 exponent that is outside the parentheses, and THEN rewrite any negative exponents that are remaining to positive ones.
     
  6. Aug 2, 2011 #5
    If i do it your way, then I get no fractions in my final answer. i just get 9a^8b^4, Sorry I dont know any other method except this recipricol one and its just not working.

    I understand your step, but what step comes after How do i turn that into a fraction again
     
  7. Aug 2, 2011 #6

    eumyang

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    You got it wrong because it looks like you think that
    [itex](-3)^{-3} = -27[/itex],
    and it's not. It should be
    [itex](-3)^{-3} = -\frac{1}{27}[/itex].

    Also, the answer book does not say that! Don't you see the typos? It should be
    [tex]-\frac{m^9 n^3}{27}[/tex]
     
  8. Aug 2, 2011 #7

    eumyang

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    No, you should have gotten
    [itex]\frac{1}{9}a^8 b^4 = \frac{a^8 b^4}{9}[/itex].
    You're not applying the negative exponent to the coefficient correctly, it seems.
     
  9. Aug 2, 2011 #8
    Cept i do realise that it is 1/-27, and yes it is a typo, but my question remains the same. Why is that mn on top and the 27 on bottom .

    When i work it out I get this...

    = 1 1
    ____ * ____
    -27m^6 n^3

    Then I dont get why the m and n are on top and 27 is on bottom. Unless the n cross multipleis up to the left and the m^6 only cross multiplies to the other side... But thats probably not it.
     
  10. Aug 2, 2011 #9
    So.. you solved it like multiplication then did a recipriocol of the "9" for the final step..?
     
  11. Aug 2, 2011 #10

    gb7nash

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    Type this instead:

    [tex ]\frac{1}{-27m^6}*\frac{1}{n^3}[/tex ]

    (without the space in the tex tags) You will save yourself and anyone who's reading your work lots of time.
     
  12. Aug 2, 2011 #11
    [tex]\frac{1}{-27m^6}*\frac{1}{n^3}[/tex]
     
  13. Aug 2, 2011 #12

    eumyang

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    But if you "distribute" the -3 exponent outside the parentheses first, you would get
    [itex]\left(-3m^{-3}n^{-1}\right)^{-3} = (-3)^{-3}m^{9}n^{6}[/itex]
    It's much easier to simplify from this, as opposed to using the reciprocal method to start.
     
  14. Aug 2, 2011 #13
    Reopen my tinypic link, and look at 3k) . How do i solve that using your method? I simplified the top half then tried solving it and it failed.

    I get to -10s^5 t^3
    __________
    4s^2 t^3

    .

    I get it this far. Now what am i supposed to do? ( I know im not using your tex thing.. I dont know how and i dont really have time at the moment)
     
    Last edited: Aug 2, 2011
  15. Aug 2, 2011 #14
    Ok, well whatever I guess. Just answer me this then. If there is an expression that include both negetive and positive exponents, I keep the positive exponents where they are and recipricol the negitive ones yes?
     
  16. Aug 2, 2011 #15

    eumyang

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    This is wrong. It's supposed to be:
    [tex]\frac{-10s^{-5}t^3}{4s^2 t^{-3}}[/tex]
    Now you can either subtract the exponents, or "flip" the variables that contain the negative exponents across the bar and make the exponents positive, like this:
    [tex]\frac{-10 t^3 t^3}{4s^2 s^5}[/tex]
    I'll leave you to do the rest.

    And if you must know, I didn't reply right away because it's morning here and I have to get ready for the day. The rest of us aren't chained to our computers 24 hours a day, you know. Now I have to run. Good luck.
     
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