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Math Help - Evaluating this fraction

  1. #1
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    Evaluating this fraction

    How would I evaluate the following fraction and express it properly?

    {\frac{2^6}{\displaystyle(\frac{1}{2^{3x}})}}

    Should I multiply and take the reciprocal of the bottom or would the brackets block me from taking the reciprocal?
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  2. #2
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    Quote Originally Posted by Kataangel View Post

    Should I multiply and take the reciprocal of the bottom
    Yep


    Quote Originally Posted by Kataangel View Post

    would the brackets block me from taking the reciprocal?
    Nah
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  3. #3
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    Disregard brackets...there just for show

    2^(3x + 6) is answer
    Last edited by Wilmer; October 1st 2009 at 08:24 PM. Reason: none
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  4. #4
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     <br />
2^6\times 2^{3x} = 2^{6+3x}<br />
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  5. #5
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    Don't get picky, pickslides
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  6. #6
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by Wilmer View Post
    Disregard brackets...there just for show
    Actually, they're not just there for show, without them the expression is ambiguous.
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  7. #7
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    Yeah that's why I thought that you couldn't reciprocate them.
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  8. #8
    Super Member Matt Westwood's Avatar
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    Well, what you can do is write it like this:

    \frac {2^6}{1} \div \frac 1 {2^{3x}}

    which is what the initial expression means.

    Then by the rule "to divide by a fraction you turn it upside down and multiply instead" you then get:

    \frac {2^6}{1} \times \frac {2^{3x}} 1

    hence the answer.

    Alternatively you can take the original expression:

    \frac {2^6}{\left({\dfrac 1 {2^{3x}}}\right)}

    ... and multiply top and bottom by the reciprocal of what's on the bottom:

    \frac {2^6 \times 2^{3x}}{\left({\dfrac 1 {2^{3x}}}\right) \times 2^{3x}}

    ... which is probably the clearest way to explain what's going on.
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  9. #9
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    Quote Originally Posted by Kataangel View Post
    How would I evaluate the following fraction and express it properly?

    {\frac{2^6}{\displaystyle(\frac{1}{2^{3x}})}}

    Should I multiply and take the reciprocal of the bottom or would the brackets block me from taking the reciprocal?
    You can also say that \frac{1}{2^{3x}} = 2^{-3x} so the expression reduces to

    \frac{2^6}{2^{-3x}}

    and then apply the laws of exponents:

    \frac{2^6}{2^{-3x}} = 2^{6-(-3x)} = 2^{6+3x}

    To go further you can factorise the exponent:

    2^{6+3x} = 2^{3(2+x)}

    And applying the laws again

    2^{3(2+x)} = (2^3)^{2+x} = 8^{2+x}
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