Comment #5 on issue 2302 by smi...@gmail.com:
2**Rational(4,5)*6**Rational(1,5) should auto-simplify to 2*3**Rational(1,5)
http://code.google.com/p/sympy/issues/detail?id=2302
What we have here is a case just opposite of power expanding which can take
a base or an exponent hint. We can either combine to give gathered bases or
gathered exponents.
wolfram alpha gives the latter form for all inputs of your example.
The "relatively prime" makes sense. What we want to know, then, is whether
B**(1/e) has a B such that B = b1**e1*b2**e2 where any gcd(ei, e) is not 1.
So factoring the base and checking for this condition should allow us to
canonicalize (not canonize) the powers.
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