a) [tex]|v|^{-1}=\frac{1}{|v|}=\frac{1}{|-2\sqrt{3}|}=\frac{1}{2\sqrt{3}}=\frac{\sqrt{3}}{6}[/tex]
b) [tex]u*v=4\sqrt{6}*(-2\sqrt{3})=-8*\sqrt{6*3}=-8\sqrt{2*3^{2}}=-24\sqrt{2}[/tex]
c)[tex]\frac{u}{v}=\frac{4\sqrt{6}}{-2\sqrt{3}}=-2\frac{\sqrt{6}}{\sqrt{3}}=-2\frac{\sqrt{2}*\sqrt{3}}{\sqrt{3}}=-2\sqrt{2}[/tex]
d)[tex]v^{3}=(-2\sqrt{3})^{3}=(-2\sqrt{3})^{2}*(-2\sqrt{3})=4*3*(-2\sqrt{3})=-24*\sqrt{3}[/tex]