Prove that $2^{(log(n)^{1/2})}$ is $O(n^a)$
$n^a = \exp(a \ln n) = \exp(a \ln n \frac{\ln 2}{\ln 2}) = 2^{\frac{a \ln n}{\ln 2}}$. Can you prove that if $h(n) = O(k(n))$ then $2^{h(n)} = O(2^{k(n)})$ ?