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Homework Help: Dividing Powers

  1. Dec 31, 2009 #1
    Can anybody talk me through the righ way to approach this problem? I know that the answer is 8.79 x 10 to the power of 5.

    7.23 x 10 to the power of 5 x 1.09 x 10 to the power of minus 3
    ______________________________________________________ (divided by)

    8.97 x 10 to the power of minus 4

    Thanks
     
  2. jcsd
  3. Dec 31, 2009 #2
    What is 102 x 10-3, for instance?
     
  4. Dec 31, 2009 #3
    10-1 (to the power of minus 1)??
     
  5. Dec 31, 2009 #4
    Yes, that's right! So what would 10a x 10b be (where a and b are any number)?
     
  6. Dec 31, 2009 #5
    My understanding is that you add the powers but use normal multiplication with the main numbers. So would it be: 100 a+b (a+b as powers)?
     
  7. Dec 31, 2009 #6
    Not quite, otherwise in your first example you would have written 100-1, wouldn't you?
     
  8. Dec 31, 2009 #7
    10 a+b
     
  9. Dec 31, 2009 #8
    Got it! So how about 106/102 ?
     
  10. Dec 31, 2009 #9
    To divde you suntract the powers so, 10 4?
     
  11. Dec 31, 2009 #10
    Going well so far, so 10a/10c = ?
     
  12. Dec 31, 2009 #11
    10 a-c
     
  13. Dec 31, 2009 #12
    Yeap, so 10a x 10b / 10c = ?
     
  14. Dec 31, 2009 #13
    10 a+b-c?
     
  15. Dec 31, 2009 #14
    Indeed, so 105 x 10-3 / 10-4 = ?
     
  16. Dec 31, 2009 #15
    10 5 x 10-3 = 10 2
    10 2 / 10 -4 = 10 -2
     
  17. Dec 31, 2009 #16
    No, remember for division 10a/10c you subtract c from a, as per posts 8 to 11, so 102/10-4 = ?
     
  18. Dec 31, 2009 #17
    But 2 - 4 = -2 so why is it incorrect to say 10 2 / 10 -4 = 10 -2? All I have done is to subtract -4 from 2.
     
  19. Dec 31, 2009 #18
    You are not doing the sum 2 - (+)4, you are doing 2 - -4. Perhaps another way to look at it is how much warmer is 2°C than -4°C? Is that 2°C ?
     
  20. Dec 31, 2009 #19
    No, it is 6°C. I know that 2 - (-4) = 6 so is the answer to 10 2 /10 -4 = 10 6?
    Thanks for your help and patience by the way!
     
  21. Dec 31, 2009 #20
    I'm starting to get it now and I can see where I went wrong the 1st time.
    If you work out the decimal figures and the figures with powers separately you get;
    0.879 x 10 to the power of 6.
    In order to present the answer as a number larger than 1 we have remove one of the powers and used it to multiply 0.879 by 10, leaving us with 8.79 x 10 5.
    Thanks again for all your help and patience.
     
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