3^(99!)<(3^99)!=3^99*(3^99-1)*(3^99-2)*(3^99-3)*...(3^99-2*3^98)....=3^99*(3^99-1)*(3^99-2)*(3^99-3)*...*(3^98)*(3-2)*....*(3^97)*(3-2)*....

That is, the righthand expression contains all the lefthand expression's factor, plus a lot more (the ellipses...):

=3^99*...*3^98*...*3^97*...*....*...*3^2*3^1

QED