The following equation (which actually evaluates to zero) is not being simplified to zero by Mathematica. I have tried the commands known to me, like Simplify, FullSimplify, Cancel, etc. The equation is given below in InputForm. The image of the equation from Mathematica is also given below.
\[Rho]^3 (Subscript[r, to]/\[Rho])^((
6 Subscript[\[Gamma], 1])/(\[Beta] +
2 Subscript[\[Gamma], 1])) (\[Beta] +
2 Subscript[\[Gamma],
1])^3 - (\[Rho] (\[Beta] + 2 Subscript[\[Gamma], 1]))^((
3 \[Beta])/(\[Beta] +
2 Subscript[\[Gamma], 1])) (Subscript[r,
to] (\[Beta] + 2 Subscript[\[Gamma], 1]))^((
6 Subscript[\[Gamma], 1])/(\[Beta] + 2 Subscript[\[Gamma], 1]))
How do I get Mathematica to evaluate this to zero? Original Expression Image
I thought the problem could be with addition and cancellation of exponents. So I tried this simpler expression given below:
(\[Beta] + 2 Subscript[\[Gamma], 1])^((
3 \[Beta])/(\[Beta] +
2 Subscript[\[Gamma], 1])) (\[Beta] + 2 Subscript[\[Gamma], 1])^((
6 Subscript[\[Gamma], 1])/(\[Beta] + 2 Subscript[\[Gamma], 1]))
This worked fine, as can be see in the image. Image with Simpler expression
How can we make Mathematica cancel and evaluate the original expression to zero? Thanks in advance.
Apparently needs some assumptions
expr = ρ^3 (Subscript[r, to]/ρ)^((
6 Subscript[γ, 1])/(β +
2 Subscript[γ, 1])) (β +
2 Subscript[γ, 1])^3 - (ρ (β + 2 Subscript[γ, 1]))^((3 β)/(β +
2 Subscript[γ, 1])) (Subscript[r, to] (β + 2 Subscript[γ, 1]))^((
6 Subscript[γ, 1])/(β + 2 Subscript[γ, 1]))
FullSimplify[expr, Assumptions ->
β > 0 && Subscript[γ, 1] > 0 &&
ρ > 0 && Subscript[r, to] > 0]
0
FullSimplify[expr, Assumptions -> ρ > 0 && Subscript[r, to] > 0]
0