${2^{logn^{logn}}} = 2^{log (n^{log \space n})} = 2^{(log \space n)log \space n} $
$2^{(log n)log n} $ NOT EQUAL TO $2^{(log n)(log n)} \space or \space 2^{(log n)^2}$
example if $n=2^{1024}$ then $2^{(log n)log n} = 2^{(log {2^{1024}})log \space 2^{1024}} = 2^{1024*10} $
and $2^{(log n)(log n)} = 2^{(log 2^{1024})(log 2^{1024})} = 2^{(1024)*(1024)}$
also $h = n^{log \space n}= (2^{1024})^{log (2^{1024})} = (2^{1024})^{10} = (2^{1024})* (2^{1024})*(2^{1024}) ...$10 times so $(2^{1024})^{10} = (2^{1024*10}) $