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Discussion in 'Mathematics' started by elizabeth1972, Jun 5, 2012.

  1. I'm a primary teacher helping my Y10 son to revise for his modular GCSE maths exams.
    Could any kind soul please explain to me in a way I can re-explain to him...

    Write as a power of 4
    45 x 47 (45)3

    and, find the value of n
    <font face="Calibri"></font>3n = 1/9 Any help would be very gratefully recevied!


     
  2. I'm a primary teacher helping my Y10 son to revise for his modular GCSE maths exams.
    Could any kind soul please explain to me in a way I can re-explain to him...

    Write as a power of 4
    45 x 47 (45)3

    and, find the value of n
    <font face="Calibri"></font>3n = 1/9 Any help would be very gratefully recevied!


     
  3. maths126

    maths126 New commenter

    Often the best way to understand these is to write them out in full initially, rather than rush to apply some fancy rule or short cut straight away without thinking.
    4^5 = 4 x 4 x 4 x 4 x 4
    4^7 = 4 x 4 x 4 x 4 x 4 x 4 x 4
    Multiplying these two together:
    = 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4
    = 4 ^ 12
    Notice that this is the same as 4^(5+7) - the 'add the powers' rule.

    (4^5)^3 = (4^5) x (4^5) x (4^5)
    = 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4
    = 4^15
    Notice that this is the same as 4^(5*3) - the 'multiply the powers' rule.

    For the last one, it's a good idea to start on the right.
    (1/9) = (1/3) x (1/3)
    But we know that (1/3) can be written as 3^(-1)

    So we have (1/9) = 3^(-1) x 3^(-1)
    Applying the 'add the powers' rule, we now get:

    3^( (-1) + (-1) )
    = 3^(-2)

    So we have found n.
     
  4. CarrieV

    CarrieV Lead commenter

    I'm primary too but I think this is right!

    4^5 is 4x4x4x4x4
    4^7 is 4x4x4x4x4x4x4
    so 4^5x4^7 is 4x4x4x4x4x4x4x4x4x4x4x4 which is 4^12
    4^5 is 4x4x4x4x4
    so 4^5 cubed is (4x4x4x4x4) x(4x4x4x4x4) x(4x4x4x4x4)
    which is 4^15
    3^2=1x3x3=9
    3^1=1x3=3
    3^0=0x3=0
    3^-1=1/3
    3^-2=1/(3x3) =1/9
     
  5. Colleen_Young

    Colleen_Young Occasional commenter

    45 x 47
    4x4x4x4x4 x 4x4x4x4x4x4x4 = 412
    if you think about it - just add the powers when multiplying (assuming base number is the same).

    (45)3
    = 45 x 45 x 45
    = 4x4x4x4x4 x 4x4x4x4x4 x 4x4x4x4x4 = 415
    power to a power - multiply the indices
    for the rules of indices, have a look at David's PowerPoint on Laws of Indices here
    Need to work out how to format answer to last question!



     
  6. CarrieV

    CarrieV Lead commenter

    It took me ages to type that out and someone got there first[​IMG]
     
  7. Colleen_Young

    Colleen_Young Occasional commenter

    3 replies all at about the same time!
     
  8. This is what I thought, but my son is convinced that he's trying to find an answer where the "power" is 4, e.g. x^4 ?????

     
  9. Colleen_Young

    Colleen_Young Occasional commenter

    All the above replies are correct answers to your questions. It's 4 to the power what?!
    The power is not 4.
    See Craig Barton's notes - scroll down to negative indices for help with your third question.
     
  10. ...and not one of them saying "Do you really not know that as the first one is a C grade GCSE question?"
    Good responses by people.
     
  11. I did know the answer to the first one, but my son had me convinced I was wrong.
    Thanks for all the help - we were trying to make it more difficult than it was here!
     
  12. Colleen_Young

    Colleen_Young Occasional commenter

    abed mymaths is a paid for subscription service - there is no way you should be publishing login details here - I suggest you ask TES to remove this very fast.

     
  13. Thanks, but we have a mymaths login though his school. We were just getting panicky because I thought I knew how to work it out (and it seems that I was right!) but he was trying to convince me otherwise.


     

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