expr = (Sqrt[s \[Gamma]^3]γ^3] + 2 Sqrt[s \[Gamma]^7]γ^7] + Sqrt[s^5 \[Gamma]^7]γ^7] + Sqrt[s \[Gamma]^11]γ^11] + 2 s (Sqrt[s \[Gamma]^5]γ^5] + Sqrt[s \[Gamma]^9]γ^9]))/(\[Gamma]γ (1 + s \[Gamma]γ + \[Gamma]^2γ^2)^2); Simplify[PowerExpand[expr]] 
expr = (Sqrt[s \[Gamma]^3] + 2 Sqrt[s \[Gamma]^7] + Sqrt[s^5 \[Gamma]^7] + Sqrt[s \[Gamma]^11] + 2 s (Sqrt[s \[Gamma]^5] + Sqrt[s \[Gamma]^9]))/(\[Gamma] (1 + s \[Gamma] + \[Gamma]^2)^2); Simplify[PowerExpand[expr]]
expr = (Sqrt[s γ^3] + 2 Sqrt[s γ^7] + Sqrt[s^5 γ^7] + Sqrt[s γ^11] + 2 s (Sqrt[s γ^5] + Sqrt[s γ^9]))/(γ (1 + s γ + γ^2)^2); Simplify[PowerExpand[expr]]