[latex](5^{log_{5}( \sqrt{3} +8)}-3^{log_{9}( \sqrt{3}-8)^{2})^{2}[/latex]

[latex]=( \sqrt{3}+8-3^{log_{3^2}( \sqrt{3}-8)^2} )^2= \\ \\ =( \sqrt{3}+8-3^{ \frac{1}{2}log_{3}( \sqrt{3}-8 )^2 } )^2= \\ \\ =( \sqrt{3}+8- \sqrt{3^{log_{3}( \sqrt{3}-8 )^2}} )^2= \\ \\ =( \sqrt{3}+8- \sqrt{( \sqrt{3}-8 )^2} )^2= \\ \\ =( \sqrt{3} +8-| \sqrt{3}-8 |)^2= \\ \\ =( \sqrt{3}+8-(-( \sqrt{3}-8 )) )^2= \\ \\ =( \sqrt{3}+8+ \sqrt{3}-8 )^2=(2 \sqrt{3} )^2=4*3=12[/latex]