The ratio of the co-efficient to $x^{15}$  to the term independent of x in the expansion of ${(x^2+\frac{2}{x})}^{15}$   is

in the expansion of ${(x^2+\frac{2}{x})}^{15}$  

General term is $T_{r+1}={ }^{15}{C}_r{\left(x^2\right)}^{15-r}{\left(\frac{2}{x}\right)}^r{=}^{15}{C}_r\left(2^r\right)\left(x^{30-3r}\right)$

$\frac{coefficient of x^{15}}{term independent of x}=\frac{{ }^{15}{C}_5\left(2^5\right)}{{ }^{15}{C}_{10}\left(2^{10}\right)}=\frac{1}{32}$