Dieter,
I recall that you've worked on the simplification of products of radicals in
the past.
On the other hand, I don't remember if there was ever any discussion of the
case sqrt(6)/sqrt(2). In current Maxima, this isn't simplified by the
general simplifier or by ratsimp -- you have to use rootscontract or radcan.
I don't know if it's always been like this or not, but it is a surprise
nonetheless.
I think it would be desirable for x^a*y^-a (where x and y are integer
constants) to simplify in the general simplifier to the same thing as
(x/y)^a. For that matter, the more general cases 18^(3/5)*48^(-4/5)
=> 3^(2/5)/2^(13/5) and even 18^(3/5)*48^(-3/7) => 3^(27/35)/2^(39/35) are
straightforward enough to handle (cf. radcan). There may be an argument
that this last case is too radical change in form, and it will surprise our
users, but then 18^3/48^4 already gets simplified to 9/8192.
-s