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Math Help - Working with Fractional Powers

  1. #1
    Member cmf0106's Avatar
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    Working with Fractional Powers

    Not sure how to solve the last part of this problem. The original equation reads:

     \sqrt{xy^3} (\sqrt{x^5y} - \sqrt{xy^7})

    So then you raise the powers to get some nicer exponents to work which looks like this

    x^\frac{1}{2}y^\frac{3}{2}(x^\frac{5}{2}y^\frac{1}  {2}) - x^\frac{1}{2}y^\frac{3}{2}(x^\frac{1}{2}y^\frac{7}  {2})

    and here is where I am lost, the author adds the exponents of the variables and ends up with

    x^\frac{6}{2}y^\frac{4}{2}-x^\frac{2}{2}y^\frac{10}{2}

    How is the author getting x^6/2, y^4/2 when you distribute for the first part of the equation? I am completely clueless as to how she did this could someone please fill me in. Thanks!
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by cmf0106 View Post
    Not sure how to solve the last part of this problem. The original equation reads:

     \sqrt{xy^3} (\sqrt{x^5y} - \sqrt{xy^7})

    So then you raise the powers to get some nicer exponents to work which looks like this

    x^\frac{1}{2}y^\frac{3}{2}(x^\frac{5}{2}y^\frac{1}  {2}) - x^\frac{1}{2}y^\frac{3}{2}(x^\frac{1}{2}y^\frac{7}  {2})

    and here is where I am lost, the author adds the exponents of the variables and ends up with

    x^\frac{6}{2}y^\frac{4}{2}-x^\frac{2}{2}y^\frac{10}{2}

    How is the author getting x^6/2, y^4/2 when you distribute for the first part of the equation? I am completely clueless as to how she did this could someone please fill me in. Thanks!
    The 1st term looks like this:

    x^\frac{1}{2}y^\frac{3}{2}(x^\frac{5}{2}y^\frac{1}  {2})

    To find the new exponent of x, add the two different exponents because this property holds:

    x^a * x^b = x^{a+b}

    Therefore: \frac{1}{2}+\frac{5}{2}=3, and the new exponent for x is 3. Likewise, y now has an exponent of 2.
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  3. #3
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    Hello,

    Quote Originally Posted by cmf0106 View Post
    Not sure how to solve the last part of this problem. The original equation reads:

     \sqrt{xy^3} (\sqrt{x^5y} - \sqrt{xy^7})

    So then you raise the powers to get some nicer exponents to work which looks like this

    x^\frac{1}{2}y^\frac{3}{2}(x^\frac{5}{2}y^\frac{1}  {2}) - x^\frac{1}{2}y^\frac{3}{2}(x^\frac{1}{2}y^\frac{7}  {2})

    and here is where I am lost, the author adds the exponents of the variables and ends up with

    x^\frac{6}{2}y^\frac{4}{2}-x^\frac{2}{2}y^\frac{10}{2}

    How is the author getting x^6/2, y^4/2 when you distribute for the first part of the equation? I am completely clueless as to how she did this could someone please fill me in. Thanks!
    The rule states : a^b a^c=a^{b+c}

    x^{\frac 12}y^{\frac 32}(x^{\frac 52}y^{\frac 12})=x^{\frac 12}y^{\frac 32}x^{\frac 52}y^{\frac 12}=x^{\frac 12}x^{\frac 52}y^{\frac 32}y^{\frac 12}=\dots
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  4. #4
    Member cmf0106's Avatar
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    Thanks for the input everyone! I just realized I made a mistake. At times I forgot the author assumes that one is not utilizing a calculator.

    1/2+5/2 she had 6/2

    I just punched it in the calculator and got 3 and skipped one of her steps. Very stupid of me for not seeing this earlier, thanks!
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