The expression

$\displaystyle \sqrt{3} * \sqrt[-4]{3}$

1.can be multiplied because

Expressions with radicals can be multiplied or divided as long as the root powerorvalue under the radical is the same.

resulting in $\displaystyle \sqrt[-4]{9}$?

2. and just for fun how in the world would you divide

$\displaystyle \sqrt{3} / \sqrt[-4]{3}$?