its false....say F1=2^2n and F2=2^n
take log on both function we get
F1=2n*log(2) F2=n*log(2).....as (log 2=1..)
we get F1=2n and F2=n.......putting large values for n=1024...
F1=2048 and F2=1024......
means F1 is asymptotically larger than F2...
so given statement is false.