[tex]\boxed{3.}~ \Big (\frac{x^{-4}}{x^{-1} \cdot x^3} \Big)^{-2} = \Big( \frac{x^{-4}}{x^{2}} \Big)^{-2}= (x^{-6})^{-2}=x^{12}. \\ \\ \boxed{4.}~ \frac{\sqrt{3}}{ \sqrt{3}- \sqrt{2}}= \frac{\sqrt{3}( \sqrt{3}+ \sqrt{2})}{( \sqrt{3}- \sqrt{2})( \sqrt{3}+ \sqrt{2})}= \frac{3+ \sqrt{6}}{3-2}=3+ \sqrt{6}. [/tex]