Radix sort sorts numbers from LSB to MSB one column of digits at a time.
Each sort of a column (imagine a Matrix where each row is a candidate number) takes $O(n)$ time
Hence total time complexity would be $O(pn)$ where p = number of columns or the word length.
The maximum number we'd require to sort would be $n^k$. (given)
The word length of such a number would be $log (n^k)$ or $klogn$ or $O(logn)$ because k is independent of n.
Hence p = $O(logn)$
So, time complexity of radix sort here would be $O(pn) = O(nlogn)$
Option C