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Math Help - Changing fractions to a power

  1. #1
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    Changing fractions to a power

    Please advise if you can.

    I am given a fraction, 1/128 and asked to give the answer as a power of 2.

    If I divide this number I get 0.00078125, which I am sure is not right.

    Powers to me are all about 10^ something, what I am struggling with here is how to turn a fraction into a power?

    Can anyone please advise

    Thanks

    David
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  2. #2
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    Hello,

    How about \left(\frac{1}{8\sqrt{2}} \right)^{2} ?
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  3. #3
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    128 = 2 \times 2  \times 2  \times 2  \times 2  \times 2  \times 2  = 2^7

    so
    128=\frac{1}{2^{7}} = 2^{-7}

    What you wrote is correct but is not completely simplified (8, for example, can be written as 2^3. and \sqrt{2}^2 = 2)

    So starting from your answer:

    \left(\frac{1}{8\sqrt{2}} \right)^{2}

    = \frac{1^2}{(8\sqrt{2})^2}

    = \frac{1}{8^2 (\sqrt{2})^2}

    = \frac{1}{(2^3)^2 \times 2}

    = \frac{1}{2^6 \times 2}

    = \frac{1}{2^7}

    = 2^{-7}
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  4. #4
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    Quote Originally Posted by David Green View Post
    Please advise if you can.

    I am given a fraction, 1/128 and asked to give the answer as a power of 2.

    If I divide this number I get 0.00078125, which I am sure is not right.

    Powers to me are all about 10^ something, what I am struggling with here is how to turn a fraction into a power?

    Can anyone please advise

    Thanks

    David
    LaTex doesn't appear to be working today. Maybe it is just my reader but I will try tell you what the others are saying.

    I think what the others are trying to tell you is that powers can be of any base. In particular, powers of 2 are 2^1= 1, 2^2= 4, 2^3= 8, 2^4= 16, 2^5= 32, 2^6= 64, 2^7= 128. And, of course, negatives put the number into the denominator. So 1/128= 2^?.
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  5. #5
    Super Member bigwave's Avatar
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    Cool

    Quote Originally Posted by David Green View Post
    Please advise if you can.

    I am given a fraction, 1/128 and asked to give the answer as a power of 2.

    If I divide this number I get 0.00078125, which I am sure is not right.

    Powers to me are all about 10^ something, what I am struggling with here is how to turn a fraction into a power?

    Can anyone please advise

    Thanks

    David
    I may be misunderstanding what is meant "the answer as a power of 2" but
    but 1/128 = 2^-7 128 itself is 2^7

    latex is not working for me either...
    Last edited by bigwave; April 15th 2011 at 12:32 PM. Reason: latex is not working
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