8. The sequence $a_{n}=\frac{n^{10}}{2^{n}}(n=1,2, \cdots)$ has its maximum term at

保留源文本的换行和格式，正确的翻译结果应为：

8. The sequence $a_{n}=\frac{n^{10}}{2^{n}}(n=1,2, \cdots)$ has its maximum term at

However, to provide a more meaningful translation, the last line should be:

8. The sequence $a_{n}=\frac{n^{10}}{2^{n}}(n=1,2, \cdots)$ has its maximum term at

But to be precise and follow the instruction, the correct translation with the original format preserved is:

8. The sequence $a_{n}=\frac{n^{10}}{2^{n}}(n=1,2, \cdots)$ has its maximum term at
8. $\frac{14^{10}}{2^{14}}$ Hint: When $x=\frac{10}{\ln 2}$, $f(x)=\frac{x^{10}}{2^{x}}$ has a unique maximum value. Therefore, the maximum term
$$
\max \left(\frac{n^{10}}{2^{n}}\right)=\max \left\{\frac{(N-1)^{10}}{2^{N-1}}, \frac{N^{10}}{2^{N}}, \frac{(N+1)^{10}}{2^{N+1}}\right\},
$$

where $N=\left[\frac{10}{\ln 2}\right]=14$.