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Laws of Exponents

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  1. Oct 25, 2015 #1
    Hello, this isn't really a physics question but I'm getting pretty desperate and you guys have always been able to help me out before :)

    1. The problem statement, all variables and given/known data

    http://imgur.com/mYtJDLI

    2. Relevant equations
    I believe I'm suppose to use the Laws of Exponents.
    For the first set possibly indices-intro-6.jpg but not sure as its addition in the question but can't find any laws with revolve around addition.

    for the second set of questions i'm fairly certain its indices-intro-6.jpg once again but I'm just not 100% sure and I'm also not 100% sure what the question is actually asking.



    3. The attempt at a solution
    3.2 + 0.007 = 3.27
    10 x -4 + 10-2 = 10-6
    3.27 x 10-6

    for the second set.
    82x 2-3=
    82= 64
    2-3= 0.125
    64 x 0.125 = 8
    But now I'm not sure what to write, it asks for it as a power of 2? Does it just mean write 23.

    If anyone could help would be greatly appreciated.
     
  2. jcsd
  3. Oct 25, 2015 #2

    SteamKing

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    I don't think the problem wants you to convert 82 and 2-3 to decimals, but instead express each number as a power of 2.

    Expressing 2-3 as a power of 2 is easy.

    Can you express 8 as a power of 2?

    If you can, then what would 82 be expressed as a power of 2?

    Once you do this, then what is the product of 82 and 2-3, evaluated using the laws of exponents?
     
  4. Oct 25, 2015 #3

    SammyS

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    That's incorrect. If you check it with a calculator you'll see that.

    For sure, 10 x -4 + 10-2 is 1/10000 + 1/100. That definitely is not 1/1000000 .

    You are to add:
    3.2×10-4 + 0.07×10-2
    This similar to adding "like" terms, but those terms are not alike.

    Rewrite one or both of them.

    For instance, 0.07 = 7×10-2, so 0.07×10-2 = 7×10-2×10-2=7×10-4. Right?

    Now both terms are alike, so you can add coefficients.
     
  5. Oct 25, 2015 #4

    haruspex

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    That is completely wrong, I'm sorry to say.
    What is 3.2 x 10-4 as a decimal number?
     
  6. Oct 25, 2015 #5
    Would 82 be 26?
    so the answer would be?
    26 x 2-3 = 26+-3
     
  7. Oct 25, 2015 #6
    0.00032 but people in another thread are telling me not to convert into decimals?
     
  8. Oct 25, 2015 #7

    SammyS

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    Don't post the same thread in more than one place !
    Mod note: I merged the two threads into a single thread here.
     
    Last edited by a moderator: Oct 26, 2015
  9. Oct 25, 2015 #8

    haruspex

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    For this problem you must do some conversion to decimals, though there is a slightly neater way than I'm suggesting you use. Let's get you to the point of finding the right answer first, then we can revisit that.
    Please post a link to the other thread.
     
  10. Oct 25, 2015 #9
    Ok thanks :)
     
    Last edited by a moderator: Oct 26, 2015
  11. Oct 25, 2015 #10
    Yeah sorry wasn't 100% sure where to post it, so it posted in two places
     
  12. Oct 25, 2015 #11

    haruspex

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    The advice not to convert to decimals was for the second question. For addition and subtraction you do, for multiplication and division you don't.
     
    Last edited by a moderator: Oct 26, 2015
  13. Oct 25, 2015 #12

    haruspex

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    It clearly belongs in precalc math, it is not a physics question.
    Mod note: Merged the two threads into the one here in precalc.
    If you feel it necessary to post on two forums (but it never should be) at least post one thread as a link to the other so that all the responses go on the same thread.
     
    Last edited by a moderator: Oct 26, 2015
  14. Oct 25, 2015 #13
    Oh yes, sorry.

    For the first one is it:
    3.2 x 10-4 = 0.00032
    0.07 x 10-2 = 0.0007
    0.00032 + 0.0007 = 0.00102?
     
  15. Oct 25, 2015 #14

    haruspex

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    Yes.
    The neater method I mentioned I see has already been described to you by SammyS in the other thread. It consists of extracting a power of 10 as a common factor. This makes the expansion to decimals a bit easier.
     
  16. Oct 25, 2015 #15

    SteamKing

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    Which is?
     
  17. Oct 25, 2015 #16
    23?
     
  18. Oct 25, 2015 #17

    SteamKing

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    Correct.
     
  19. Oct 25, 2015 #18
    The question does state to show how I manipulated the powers of 10, would it be possible for you to explain this other method as I don't really understand the other explanation.

    Thank you for you help so far :)
     
  20. Oct 25, 2015 #19

    haruspex

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    I'll make it general and see if you can figure out how to apply it to the question.
    Suppose you have a.nb+c.nd. Note that the bases of both exponentiated factors are n.
    This allows you to take out a common factor of the form nk, for any k you choose.
    a.nb=a.nb-k.nk (use the law of exponents you quoted to check this).
    a.nb+c.nd=a.nb-k.nk+c.nd-k.nk=(a.nb-k+c.nd-k).nk.
    We choose k=d:
    (a.nb-d+c).nd.
    Now all you have to do is write out a.nb-d as a decimal and add c to it.
     
  21. Oct 26, 2015 #20
    Sorry for replying so late, this took me a while to understand. Is this correct:
    3.2 = 32000 x 10-4
    10-4 + 10-4 = 10-8

    0.07 = 7 x 10-2
    10-2 + 10-2 = 10-4

    32000 x 10-8 + 7 x 10-4
     
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