[Number Theory]
Problem: Let $T=20$. The product of all positive divisors of $2^{T}$ can be written in the form $2^{K}$. Compute $K$.

Solution: When $n$ is a nonnegative integer, the product of the positive divisors of $2^{n}$ is $2^{0} \cdot 2^{1} \cdot \ldots \cdot 2^{n-1} \cdot 2^{n}=$ $2^{0+1+\cdots+(n-1)+n}=2^{n(n+1) / 2}$. Because $T=20$ is an integer, it follows that $K=\frac{T(T+1)}{2}=\mathbf{2 1 0}$.

Final answer: 210