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Math Help - Function Operations and Compositions

  1. #1
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    Function Operations and Compositions

    Please help me to simplify this expression. . .

    The original equation is
    11^(2/5)
    11^(4/5)
    I actually worked it to the point I got:
    1
    121^(1/5)
    Can you show me or tell me how to solve this to where there is no rational # on bottom?
    Last edited by runner940; March 31st 2009 at 04:27 PM.
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  2. #2
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    Quote Originally Posted by runner940 View Post
    Please help me to simplify this expression. . .

    The original equation is
    11^(2/5)
    11^(4/5)
    I actually worked it to the point I got:
    1
    121^(1/5)

    Can you show me or tell me how to solve this to where there is no rational # on bottom?

    Multiply by \frac{121^{\frac{4}{5}}}{121^{\frac{4}{5}}} (a cleverly disguised 1)
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  3. #3
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    Quote Originally Posted by runner940 View Post
    The original [expression] is \frac{11^{\frac{2}{5}}{11^{\frac{4}{5}}.

    I actually worked it to the point I got: \frac{1}{121^{\frac{1}{5}}.

    Can you show me or tell me how to solve this to where there is no rational # on bottom?
    Try using exponent rules:

    . . . . . \frac{x^m}{x^n}\, =\, x^{m\, -\, n}

    In your case, this means that the original expression simplifies as 11^{-\frac{2}{5}}\, =\, \frac{1}{(11^2)^{\frac{1}{5}}}, as you mention.

    Now you need to rationalize the radical denominator.

    Hint: To be able to take the 121 out of the radical (the fifth root that is indicated by the one-fifth power), you need four more copies of 121 inside the root. So what should you multiply by?

    Highlight the space below for a bigger hint.

    \huge\color{white}\frac{121^{\frac{4}{5}}}{121^{\f  rac{4}{5}}}

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