Let $\{a,b,c,d,e,f,g,h,i\}$ be a permutation of $\{1,2,3,4,5,6,7,8,9\}$ such that $\gcd(c,d)=\gcd(f,g)=1$ and
\[(10a+b)^{c/d}=e^{f/g}.\]
Given that $h>i$, evaluate $10h+i$.

Let's think step by step and output the final answer within \boxed{}.
user