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2

Others are certainly correct in pointing out that (x^3)^(1/3) is only equal to x under certain circumstances. But if you know that, and just want to simplify while assuming that x is positive, then just use PowerExpand PowerExpand[(x^3)^(1/3)] (* x *) PowerExpand[(x^3 y^3 z)^(1/3)] (* x y z^(1/3) *)


2

Well, it's not generally true. For example: ((-1)^3)^(1/3) N[%] (* Out: (-1)^(1/3) 0.5 + 0.866025 I *) I suppose you could do FullSimplify[(x^3 y^3 z)^(1/3), Assumptions -> {x > 0, y > 0, z > 0}] (* Out: x y z^(1/3) *)


0

This seems to work although I have not tested it thoroughly. Also, it's a rather brute force approach, so I hope someone else will post a more elegant solution. g[0] = {{Θ, 0, 0, 0, T, 0}, {u Θ, ρ, 0, 0, T u, 0}, {v Θ, 0, ρ, 0, T v, 0}, {w Θ, 0, 0, ρ, T w, 0}, {-1 + H Θ, u ρ, v ρ, w ρ, H T + ρ Ω, (5 ρ)/3}, {k Θ, 0,0, 0, k T, ρ}} ...



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