GCSE Maths Indices

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  1. SweatyGoldfish's Avatar
    1 10-06-2012  16:11
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    GCSE Maths Indices
    Could anyone explain how to answer these questions please:

    a=2^x and b=2^y

    Express in terms of a and b.

    i) 2^(x+y)

    ii)2^2x

    ii)2^(x+2y)
  2. SubAtomic's Avatar
    2 10-06-2012  16:14
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    Re: GCSE Maths Indices
    i) \displaystyle 2^{x+y}= 2^x2^y

    Any clearer?

    Can you go from this and answer ii) and iii) ?
    Last edited by SubAtomic; 10-06-2012 at 16:17.
  3. oh_1993's Avatar
    3 10-06-2012  16:15
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    Re: GCSE Maths Indices
    For i) use x^(a+b) = x^a*x^b
    ii) Use x^(ab) = (x^a)^b
    iii) Combination of the two above.
  4. SweatyGoldfish's Avatar
    4 10-06-2012  16:17
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    Re: GCSE Maths Indices
    (Original post by SubAtomic)
    i) \displaystyle 2^{x+y}= 2^x2^y

    Any clearer?
    Would this not make 4^(x+y)?

    Or do you not multiply the 2's?

    EDIT: DISREGARD THIS I AM AN IDIOT
    Last edited by SweatyGoldfish; 10-06-2012 at 16:21.
  5. SubAtomic's Avatar
    5 10-06-2012  16:19
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    Re: GCSE Maths Indices
    (Original post by SweatyGoldfish)
    Would this not make 4^(x+y)?

    Or do you not multiply the 2's?
    No because 2 is the common factor. Do you know index laws? Link

    \displaystyle a=2^x \ , \ b=2^y

    x and y are powers, 2 is the common multiple.


    (Original post by SweatyGoldfish)
    EDIT: DISREGARD THIS I AM AN IDIOT
    You get it now then?
    Last edited by SubAtomic; 10-06-2012 at 16:26.
  6. SweatyGoldfish's Avatar
    6 10-06-2012  16:28
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    Re: GCSE Maths Indices
    (Original post by SubAtomic)
    No because 2 is the common factor. Do you know index laws? Link

    \displaystyle a=2^x \ , \ b=2^y

    x and y are powers, 2 is the common multiple.




    You get it now then?
    Yeah I realised as I wrote it that I was wrong.

    So would the first answer be = ab?

    Just trying to work out the other two now.
  7. SubAtomic's Avatar
    7 10-06-2012  16:29
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    Re: GCSE Maths Indices
    (Original post by SweatyGoldfish)
    Yeah I realised as I wrote it that I was wrong.

    So would the first answer be = ab?

    Just trying to work out the other two now.
    Yep, use what I gave in post 2 to rewrite the equation.
    Last edited by SubAtomic; 10-06-2012 at 16:30.
  8. SweatyGoldfish's Avatar
    8 10-06-2012  16:33
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    Re: GCSE Maths Indices
    (Original post by SubAtomic)
    Yep, use what I gave in post 2 to rewrite the equation.
    My brains in meltdown because I've been revising for about 4 hours straight, would you mind just answering the other two questions and explaining how to do them/how you got the answers?
  9. SubAtomic's Avatar
    9 10-06-2012  16:36
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    Re: GCSE Maths Indices
    (Original post by SweatyGoldfish)
    My brains in meltdown because I've been revising for about 4 hours straight, would you mind just answering the other two questions and explaining how to do them/how you got the answers?
    Will help you do ii)

    \displaystyle 2^{x+x}=2^x2^x=2^{2x}

    Any better? What do you do when you multiply something by itself?

    Spoiler:
    Show


    And for iii) You have

    \displaystyle 2^x2^{y+y}=2^x2^y2^y=2^{x+2y}

    Any better?
    Last edited by SubAtomic; 10-06-2012 at 16:41.
  10. SweatyGoldfish's Avatar
    10 10-06-2012  16:44
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    Re: GCSE Maths Indices
    So ii) is 2^x x 2^x, which is a x a, which is a^2?

    and iii) is 2^x x 2^y x 2^y, which is a x b x b, which is a x 2b?

    Bold is multiply just to make it clearer.
  11. SweatyGoldfish's Avatar
    11 10-06-2012  16:46
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    Re: GCSE Maths Indices
    (Original post by SweatyGoldfish)
    So ii) is 2^x x 2^x, which is a x a, which is a^2?

    and iii) is 2^x x 2^y x 2^y, which is a x b x b, which is a x 2b?

    Bold is multiply just to make it clearer.

    (Original post by SubAtomic)
    x
    ..
  12. SubAtomic's Avatar
    12 10-06-2012  16:47
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    Re: GCSE Maths Indices
    (Original post by SweatyGoldfish)
    So ii) is 2^x x 2^x, which is a x a, which is a^2?

    and iii) is 2^x x 2^y x 2^y, which is a x b x b, which is a x 2b?

    Bold is multiply just to make it clearer.
    Yes on part ii) but you did something different for iii) why did you change the rule you used in the previous question? \displaystyle 2 \times b \ \mathrm{isn't} \ b \times b

    (Original post by SweatyGoldfish)
    ...
    Yep you got it:cool:

    so you have

    \displaystyle i) \ ab \ , \ ii) \ a^2 \ , iii) \ ab^2
    Last edited by SubAtomic; 10-06-2012 at 16:57.
  13. SweatyGoldfish's Avatar
    13 10-06-2012  16:51
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    Re: GCSE Maths Indices
    (Original post by SubAtomic)
    Yes on part ii) but you did something different for iii) why did you change the rule you used in the previous question? \displaystyle 2 \times b \ \mathrm{isn't} \ b \times b

    Sorry that was just a typo from typing it out fast, I meant a x b^2
  14. SweatyGoldfish's Avatar
    14 10-06-2012  16:56
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    Re: GCSE Maths Indices
    (Original post by SubAtomic)
    Yes on part ii) but you did something different for iii) why did you change the rule you used in the previous question? \displaystyle 2 \times b \ \mathrm{isn't} \ b \times b



    Yep you got it:cool:

    so you have

    \displaystyle i) \ ab \ , \ ii) \ a^2 \ , iii) \ ab^2

    Yep, thanks a lot for the help
  15. SubAtomic's Avatar
    15 10-06-2012  16:59
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    Re: GCSE Maths Indices
    (Original post by SweatyGoldfish)
    Yep, thanks a lot for the help
    No problem:cool:
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