\(\begin{array}{l}
{3^{4000}} = {3^{4.1000}} = {\left( {{3^4}} \right)^{1000}} = {81^{1000}}\\
{4^{3000}} = {4^{3.1000}} = {\left( {{4^3}} \right)^{1000}} = {64^{1000}}\\
Ma\,\,{81^{1000}} > {64^{1000}}\\
\Rightarrow {3^{4000}} > {4^{3000}}
\end{array}\)