6. Calculate the highest power of 2 contained in $\left(2^{n}\right)$ !.

保留源文本的换行和格式，翻译结果如下：

6. Calculate the highest power of 2 contained in $\left(2^{n}\right)$!.
6. Solution: The highest power of 2 in $\left(2^{n}\right)$ ! is $\left[\frac{2^{n}}{2}\right]+$
$$
\left[\frac{2^{n}}{2^{2}}\right]+\cdots+\left[\frac{2^{n}}{2^{n}}\right]=2^{n-1}+2^{n-2}+\cdots+1=2^{n}-1 .
$$