Solution
= Solution
The <exponential function> eventually grows faster than the fixed <polynomial>. A direct justification uses the ratio $r_n=4^n/n^4$:
$$
\frac{r_{n+1}}{r_n}=4\left(\frac n{n+1}\right)^4\longrightarrow4.
$$
For all sufficiently large $n$, this ratio exceeds $2$, so $r_n$ grows without bound. The proposed <Big O notation> bound is therefore impossible:
$$
\boxed{\text{False: }4^n\ne O(n^4).}
$$