Status: Accepted
Owner: asmeurer
Labels: Type-Defect Priority-Medium

New issue 2302 by asmeurer: 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

Currently we have:

In [294]: 2**Rational(4,5)*6**Rational(1,5)
Out[294]:
 4/5 5 ⎽⎽⎽
2   ⋅╲╱ 6

In [295]: 2*3**Rational(1,5)
Out[295]:
  5 ⎽⎽⎽
2⋅╲╱ 3

But these are the same:

In [296]: N(2**Rational(4,5)*6**Rational(1,5))
Out[296]: 2.49146187923103

In [297]: N(2*3**Rational(1,5))
Out[297]: 2.49146187923103

You can also see it by:

In [298]: 2**4*6
Out[298]: 96

In [299]: 96**Rational(1, 5)
Out[299]:
  5 ⎽⎽⎽
2⋅╲╱ 3

We auto-simplify square roots in Mul, like

In [301]: sqrt(2)*sqrt(12)
Out[301]:
    ⎽⎽⎽
2⋅╲╱ 6

so this should work too.

This is the source of the woes from issue 2226.

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