We can rewrite it as 50!/(25!*25!)
18= 3*3*2
So we must find number of 2's and 3's in 50! & 25!
2's in 50!
$\frac{50}{2}+\frac{50}{4}+\frac{50}{8}+\frac{50}{16}+\frac{50}{32}$
25+12+6+3+1=47
3's in 50!
$\frac{50}{3}+\frac{50}{9}+\frac{50}{27}$
16+5+1= 22
Similarly we find no of 2's and 3's in 25! which is 22 & 10 respectively
50!/25!*25! no of 2's= 47-44=3 no of 3's=22-20=3
so only 181 is possible
Hence highest power is 1