Problem (Algebra):
Let $T=800$. Simplify $2^{\log _{4} T} / 2^{\log _{16} 64}$.

Solution:
Note that $2^{\log _{4} T}=4^{\left(\frac{1}{2} \log _{4} T\right)}=4^{\log _{4} T^{\frac{1}{2}}}=\sqrt{T}$. Letting $\log _{16} 64=x$, we see that $2^{4 x}=2^{6}$, thus $x=\frac{3}{2}$, and $2^{x}=\sqrt{8}$. Thus the given expression equals $\sqrt{\frac{T}{8}}$, and with $T=800$, this is equal to 10 .

Final answer: 10