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How would I simplify this expression? $$\sqrt[4]{\frac{g^3h^4}{4r^{14}}}\ ?$$

I did this $$\begin{align*} \sqrt[4]{g^3h^3h^4}\\ h\sqrt[4]{g^3h^3}\\ \sqrt[4]{4r^{14}}\\ \sqrt[4]{2r^2r^{12}}\\ r^3\sqrt[4]{2r^2}\\ \end{align*}$$

But I am stuck?

Yes that is correct

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    Is the initial expression $\sqrt[4]{\dfrac{g^3 h^4}{4 r^{14} } }$ or something else?2011-09-08
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    Where did you get the extra $h^3$ in the numerator in your first step? $\sqrt[4]{g^3h^4}=h\sqrt[4]{g^3}$.2011-09-08
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    How do the series of expressions after "I did this" relate to each other?2011-09-08
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    How did $\frac{1}{4r^{14}}$ turn into $h^3$?2011-09-08
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    @anon: I edited for readability, but did not include anything extra. Seems to me the OP is first trying to simplify the numerator, $\sqrt[4]{g^3h^4}$ (alas, incorrectly, since that extra $h^3$ shouldn't be there); and then *separately* trying to simplify the denominator $\sqrt[4]{4r^{14}}$ (again, unfortunately incorrectly since the $4$ should not have become a $2$).2011-09-08
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    @Arturo: Ah, I should have seen that if I read down just a bit farther.2011-09-08

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