Posted by Victoria on Wednesday, May 14, 2008 at 1:04am.
Recognize that
16^(2*square root 2)= (4^2)^(2sqrt2)
= 4^(4sqrt2)
So your expression can be written
4^(3/sqrt2)/4^(4sqrt2)
= 4^[(3/sqrt2)-(4sqrt2)]
= 4^[(3/2)sqrt2-4sqrt2]
= 4^[-(5/2)sqrt2]
= 2(-5sqrt2)
I might have made a mistake somewhere, so be sure to verify the steps.