[tex]\displaystyle \\
\frac{3\times 2^{2013}}{16^{503}}= \frac{3\times 2^{2013}}{(2^4)^{503}}= \frac{3\times 2^{2013}}{2^{4\times 503}}= \\ \\
= \frac{3\times 2^{2013}}{2^{2012}}= 3\times 2^{2013-2012} =3\times 2^1 = 3\times 2 = \boxed{6} \\ \\ [/tex]
