Indices

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  1. krisshP's Avatar
    1 05-07-2012  16:53
    • Overlord in Training
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    Indices
    Below is a question on indices I'm stuck on.

    Write the following as a power of 2.
    2\sqrt{2}

    I don't understand how to start it off and do it and need help.:confused::confused:

    Thanks for help provided.
  2. james22's Avatar
    2 05-07-2012  16:58
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    Re: Indices
    What is 2 as a power of 2? What is sqrt(2) as a power of 2? What do you do to the powers when you multiply 2 numbers together?
    Last edited by james22; 05-07-2012 at 17:03.
  3. krisshP's Avatar
    3 05-07-2012  16:59
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    Re: Indices
    (Original post by james22)
    What is2 as a power of 2? What is sqrt(2) as a power of 2? What do you do to the powers when you multiply 2 numbers together?
    2^2=4

    square root 2 and then sqaured gives just 2.

    Add the powers.
  4. SillyEddy's Avatar
    4 05-07-2012  17:00
    • Peer Of The TSR Realm
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    Re: Indices
    How would you write '2' in terms of powers of '2'? Well 2^0 is 1. 2^1 is 2. 2^2 is 4, etc.

    How would you write 'root 2' in terms of powers of '2'? Well, it'll be a power to a fraction, you just need to remember which one.


    Then, because you're multiplying the numbers, you add the powers.
  5. james22's Avatar
    5 05-07-2012  17:01
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    Re: Indices
    (Original post by krisshP)
    2^2=4

    square root 2 and then sqaured gives just 2.

    Add the powers.
    No, I said what is 2 as a power of 2, i.e. write 2 in the for 2^x. Do the same for sqrt (2).
    Last edited by james22; 05-07-2012 at 17:04.
  6. aznkid66's Avatar
    6 05-07-2012  18:26
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    Re: Indices
    "Write down the following as a power of 2," means the same thing as "Set it equal to 2^x, find x, and write down 2^x."

    Note that, as mentioned above, 2\sqrt{2}=2\cdot\sqrt{2}.

    So if 2=2^a and \sqrt{2}=2^b, then 2\sqrt{2}=2\cdot\sqrt{2}=2^a \cdot 2^b=2^{a+b}.
    Post rating:
    2
  7. 123maz's Avatar
    7 05-07-2012  18:36
    • Exalted Member
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    Re: Indices
    The answer is 2. as I dont think you can have the square root of two so you simply square 2 which is 4, then 2 squared equals 4 so the initial answer is 2. (well i think it is )
    Post rating:
    5
  8. krisshP's Avatar
    8 05-07-2012  18:50
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    Re: Indices
    Isn't the answer 2^\frac{3}{2}???

    working out:

    2\times2^\frac{1}{2}

    The above is like saying:

    2^1\times2^\frac{1}{2}

    2/2 + 1/2 = 3/2

    Therefore isn't the answer 2^\frac{3}{2}???
  9. james22's Avatar
    9 05-07-2012  18:55
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    Re: Indices
    (Original post by krisshP)
    Isn't the answer 2^\frac{3}{2}???

    working out:

    2\times2^\frac{1}{2}

    The above is like saying:

    2^1\times2^\frac{1}{2}

    2/2 + 1/2 = 3/2

    Therefore isn't the answer 2^\frac{3}{2}???
    This is correct
  10. krisshP's Avatar
    10 05-07-2012  18:56
    • Overlord in Training
    • Posts: 2,111
    Re: Indices
    (Original post by james22)
    This is correct
    What about the following:

    \sqrt[3]{16}
    as a power of 2.
    ??
  11. aznkid66's Avatar
    11 05-07-2012  19:02
    • Exalted and Worshipped Member
    • Posts: 922
    Re: Indices
    All you need are the answers to the following questions:

    What is cbrt(x) as a power of x?

    What is 16 as a power of 2?

    What is the (x^a)^b as a power of x?

    With just that, you should be able to solve the problem.
    Last edited by aznkid66; 05-07-2012 at 19:06. Reason: Changed it to be more hint-y.
  12. TenOfThem's Avatar
    12 05-07-2012  19:03
    • No --- I am a Newbie --- Honest
    Re: Indices
    (Original post by krisshP)
    What about the following:

    \sqrt[3]{16}
    as a power of 2.
    ??
    what is 16 as a power of 2
  13. krisshP's Avatar
    13 05-07-2012  19:05
    • Overlord in Training
    • Posts: 2,111
    Re: Indices
    I got the correct answer:

    2^\frac{4}{3}

    Thanks a lot.
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