limits

Hi,

I am sorry for this stupid question - but how can I calculate the limit of:

(3**x+5**x)**(1/x)

for x->+infinity? The result is 5 as you can check by hand:

(3**x+5**x)**(1/x) = 5 * ((3/5)**x+1)**(1/x) -> 5

When I tried that in axiom:

limit((3**x+5**x)**(1/x), x=%+infinity)

or the equivalent problem:

limit((3**(1/x)+5**(1/x))**(x), x=0, "right")

I got "failed".

Also, this works correctly:

simplify(2**x * 2**(2*x))

simplifies to 2**(3x)

but this doesn't simplify at all:

simplify(2**(5*x)/2**(4*x))



Thanks,
Ondrej