is this time complexity subexponential?
It depends on how you define subexponential. The definition I generally use is:

$$\textsf{SUBEXP} = \bigcap_{\varepsilon &gt; 0}\textsf{DTIME}(2^{n^\varepsilon})$$

However some authors define:

$$\textsf{SUBEXP} = \textsf{DTIME}(2^{o(n)})$$

Since your function is $2^{n^c}$ for some constant $c&lt;1$, it would be subexponential according to the second but not to the first.