\[\boxed{\mathbf{484}.}\]
\[1)\ 5^{\sqrt{71}}\ или\ 5^{\sqrt{69}};\]
\[71 > 69;\]
\[\sqrt{71} > \sqrt{69};\]
\[5^{\sqrt{71}} > 5^{\sqrt{69}};\]
\[Ответ:\ \ 5^{\sqrt{71}}.\]
\[2)\ \left( \frac{1}{2} \right)^{\sqrt{3}}\ или\ \left( \frac{1}{2} \right)^{\sqrt{2}};\]
\[3 > 2;\]
\[\sqrt{3} > \sqrt{2};\]
\[\left( \frac{1}{2} \right)^{\sqrt{3}} < \left( \frac{1}{2} \right)^{\sqrt{2}};\]
\[Ответ:\ \ \left( \frac{1}{2} \right)^{\sqrt{2}}.\]
\[3)\ 3^{- \sqrt{3}}\ или\ 3^{- \sqrt{2}};\]
\[3 > 2;\]
\[\sqrt{3} > \sqrt{2};\]
\[- \sqrt{3} < - \sqrt{2};\]
\[3^{- \sqrt{3}} < 3^{- \sqrt{2}};\]
\[Ответ:\ \ 3^{- \sqrt{2}}.\]
\[4)\ 2^{\sqrt{3}}\ или\ 2^{1,7};\]
\[300 > 289;\]
\[\sqrt{300} > 17;\]
\[\sqrt{3} > 1,7;\]
\[2^{\sqrt{3}} > 2^{1,7};\]
\[Ответ:\ \ 2^{\sqrt{3}}.\]