[tex]\frac{2\cdot2^2\cdot...2^{2010}}{(32^{1608})^{251}}=\frac{2^{1+2+...+2010}}{((2^5)^{1608})^{251}}=\frac{2^{\frac{2010(2010+1)}{2}}}{(2^5)^{1608\cdot251}}=\\
\\
\frac{2^{1005\cdot2011}}{2^{5\cdot1608\cdot251}}=2^{1005\cdot2011-5\cdot1608\cdot251}=2^{5\cdot3(67\cdot2011-536\cdot251)}=2^{5\cdot3\cdot201} \geq 1[/tex]
