## Rationalizing Denominators

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
pieldevereda
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### Rationalizing Denominators

Hi, I can 't resolve this exercise

I have the result, but i don 't why is that

Thanks

Regards

stapel_eliz
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$\mbox{Exercise: }\, \frac{y}{\sqrt[6]{y^7}}$

$\mbox{Result: }\, \frac{\sqrt[6]{y^5}}{y}$

I have the result, but i don 't why is that
To learn how to rationalize denominators, try here.

Note: You might find it helpful to simplify the denominator first. Then cancel, and then rationalize.

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### Re: Rationalizing Denominators

Hello, to rationalize the denominator, you want to get rid of the radical at the bottom by mulitplying the top and the bottom by "1". The key to this problem is to notice the index of "6". If you attempted to solve it by using just the $\sqrt{y}$ with an index of "2" you would get a different answer.

Let's first get our number "1"

$\frac{\sqrt[6]{y^5}}{\sqrt[6]{y^5}$ = $\frac{1}{1}$

$\frac{y}{\sqrt[6]{y^7}$ * $\frac{\sqrt[6]{y^5}}{\sqrt[6]{y^5}$ = $\frac{y\sqrt[6]{y^5}}{\sqrt[6]{y^12}$

Now we need to rationalize the denominator

$\frac{y\sqrt[6]{y^5}}{\sqrt[6]{y^12}$ = $\frac{y\sqrt[6]{y^5}}{{y^2}$

The last step is to simplify the answer

$\frac{y\sqrt[6]{y^5}}{{y^2}$ = $\frac{y * \sqrt[6]{y^5}}{{y*y}$

Divide out the "y" and you should end up with your answer.

$\frac{\sqrt[6]{y^5}}{{y}$

Hope this helps.

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### Re: Rationalizing Denominators

Oops...my bad, I should have given hints and not shown the whole problem. Sorry about that. I'm new on here and won't do that again. Though, there is typically more than one way to solve a problem. I highly encourage you to attempt simplifying the problem first and then solving it.

pieldevereda
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