# Math Help - Cancelling out a root function of y

1. ## 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.

2. ## Re: Cancelling out a root function of y

can you post the equation please?

3. ## 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.

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

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.

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

So far I've got

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

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

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

6. ## 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.

7. ## 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.

8. ## Re: Cancelling out a root function of y

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