[tex]\it (3^{\sqrt5})^{\sqrt3} = 3^{\sqrt{15}} \ \textless \ 3^{\sqrt{16}} = 3^4=81 \Longrightarrow (3^{\sqrt5})^{\sqrt3} \ \textless \ 81 \ \ \ (1)[/tex]
[tex]\it (5^{\sqrt3})^{\sqrt3} = 5^{\sqrt3 \cdot \sqrt3} = 5^3 = 125 \ \ \ \ (2)[/tex]
[tex]\it (1), \ (2) \Longrightarrow (3^{\sqrt5})^{\sqrt3} \ \textless \ 81 \ \textless \ 125 = (5^{\sqrt3})^{\sqrt3} \ \ \ \ (3)[/tex]
[tex]\it (3) \Longrightarrow (3^{\sqrt5})^{\sqrt3} \ \textless \ (5^{\sqrt3})^{\sqrt3} \Longrightarrow 3^{\sqrt5} \ \textless \ 5^{\sqrt3} \ \ . [/tex]
