How to calculate O-Notation?
We can show that $O(2^n\cdot n^{10}) \not\subset O(2^n)$:
As $2^n\cdot n^{10} \in O(2^n\cdot n^{10})$, then, if also holds $2^n\cdot n^{10} \in O(2^n)$ then we will have $2^n\cdot n^{10} \leqslant C 2^n$, which gives false $n^{10} \leqslant C$.