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#1003 Exponentiation laws are missing
Take a look at
http://en.wikipedia.org/wiki/Exponentiation#Identities_and_properties
We KNOW that aⁿ × bⁿ = (a × b)ⁿ, because that is a LAW.
(That is "a^n * b^n = (a * b)^n")
This is ignored by Maxima, for instance,
(%i1) fullratsimp(7*sqrt(3)*sqrt(78));
(%o1) 7*sqrt(3)*sqrt(78)
still, 7*sqrt(3)*sqrt(78) = 7*sqrt(3*78) so the correct
answer is
(%o1) 21*sqrt(26)
--Mario/Mexico
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The function radcan does what you want:
(%i6) radcan(7*sqrt(3)*sqrt(78));
(%o6) 21*sqrt(2)*sqrt(13)
Also, a^n * b^n = (a * b)^n isn't an identity.
Try a --> -1, b --> -1, and n --> 1/2. If Maxima
automatically did a^n * b^n ==> (a * b)^n, that
would be a bug. The wikipedia article you reference
*does* say that n is an integer; in your example,
the exponent isn't an integer.