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Math Help - Cancelling out a root function of y

  1. #1
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    Cancelling out a root function of y

    Hi there,

    I've got an equation and I need to find the value of y. I've been able to get y on it's own side of the equation but am stuck on the last steps. The left side of the equation is y^{\frac{1}{4}} and I have then used the rule for powers to achieve \sqrt[4]{y} but I don't know what I need to do now to both sides of the equation to get y on it's own.

    Many thanks.
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  2. #2
    Senior Member BAdhi's Avatar
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    Re: Cancelling out a root function of y

    can you post the equation please?
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  3. #3
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    Re: Cancelling out a root function of y

    I did think that the power of 4 would do it, but Mathcad isn't giving me y on it's own.

    I'm starting to think I may have made an error in Mathcad.

    Would somebody please confirm if (\sqrt[4]{y})^{4}=y

    Many thanks.
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  4. #4
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    Re: Cancelling out a root function of y

    Quote Originally Posted by BAdhi View Post
    can you post the equation please?
    Hi, the original equation is

    \frac{-2}{y^{\frac{1}{4}}}=-(2e^{x}-e^{-2x})^{-\frac{1}{2}}+\frac{1}{2}

    Thanks.
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  5. #5
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    Re: Cancelling out a root function of y

    So far I've got

    \frac{-2}{y^{\frac{1}{4}}}=-(2e^{x}-e^{-2x})^{-\frac{1}{2}}+\frac{1}{2}

    -2=y^{\frac{1}{4}}[-(2e^{x}-e^{-2x})^{-\frac{1}{2}}+\frac{1}{2}]

    y^{\frac{1}{4}}=\frac{-2}{-(2e^{x}-e^{-2x})^{-\frac{1}{2}}+\frac{1}{2}}
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  6. #6
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    Re: Cancelling out a root function of y

    Would the next step be

    y=[\frac{-2}{-(2e^{x}-e^{-2x})^{-\frac{1}{2}}+\frac{1}{2}}]^{4}

    Thanks.
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  7. #7
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    Re: Cancelling out a root function of y

    (\sqrt[4]{y})^{4}=y

    This is correct
    A quick and easy way to check is to give y a value and check.

    so
    let y = 1000

    (\sqrt[4]{1000})^{4} put this in your calculator to check, and you should get 1000.
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  8. #8
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    Re: Cancelling out a root function of y

    Thanks for confirming, I've been able to complete the problem.
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