[tex]3^4*3^{1-\sqrt2}=3^{4+1-\sqrt2}=3^{5-\sqrt2}\\3^3:3^{2-\sqrt2}=3^{3-(2-\sqrt2)}=3^{1+\sqrt2}\\(3^{\sqrt7-\sqrt3})^{\sqrt7+\sqrt3}=3^{(\sqrt7-\sqrt3)(\sqrt7+\sqrt3)}=3^{7-3}=3^4\\(3^{\sqrt3})^{1-\sqrt3}=3^{\sqrt3(1-\sqrt3)}=3^{\sqrt3-3}\\6^{\sqrt7}:2^{\sqrt7}=(6:2)^{\sqrt7}=3^{\sqrt7}\\(\sqrt3)^{\pi}*(\sqrt3)^{\pi}=(\sqrt3*\sqrt3)^{\pi}=3^{\pi}[/tex]
