<s>[INST] Simplifying the expression $\sqrt[4]{\frac{g^3h^4}{4r^{14}}}$? 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
 [/INST] If the initial expression is $$\sqrt[4]{\dfrac{g^3 h^4}{4 r^{14} } }$$ then you have made slight errors as $\sqrt[4]{g^3 h^4} = h\sqrt[4]{g^3}$ not $h\sqrt[4]{g^3 h^3}$, while $\sqrt[4]{4 r^{14}} = r^3 \sqrt[4]{4 r^2}$ not $r^3 \sqrt[4]{2 r^2}$.
But otherwise you seem to have done sensible things.  
So you could end up with $$\frac{h}{r^3}\sqrt[4]{\dfrac{g^3 }{4 r^{2} } }$$ or write it some other way, such as $$2^{-0.5} g^{0.75} h^1 r^{-3.5}.$$  
</s>