In some paper I read,
A theoretical worst case study shows that a single regular expression of length $n$ can be expressed as an NFA with $O(n)$ states. When the NFA is converted into a DFA, it may generate O($\Sigma^n$) states. The processing complexity for each character in the inpuyt it $O(1)$ in a DFA, but is $O(n^2)$ for an NFA when all $n$ states are active at the same time.
Please explain how NFA has at its maximum just $n$ states and its equivalent DFA has at most $O(\Sigma^n)$ states?