Quick note: the [tex]\dbinom xy[/tex] expression you used is misleading and not the same as [tex]\dfrac xy[/tex].
The notations [tex]\sqrt[n]s[/tex] and [tex]s^{1/n}[/tex] are equivalent in this context:
[tex]\dfrac{\sqrt[6]s\sqrt{s^9}}{\sqrt{16s^{18}}}=\dfrac{s^{1/6}s^{9/2}}{\sqrt{16}s^{18/2}}=\dfrac{s^{1/6+9/2}}{4s^9}=\dfrac{s^{14/3}}{4s^9}=\dfrac{s^{-13/3}}4=\dfrac4{s^{13/3}}=\dfrac4{\sqrt[3]{s^{13}}}[/tex]
