\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]

↓

\[\frac{1}{\frac{\sqrt{k}}{{\left(\left(n \cdot 2\right) \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)}}}\]

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Derivation

Initial program 0.5
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
Initial simplification0.4
\[\leadsto \frac{{\left(\left(n \cdot 2\right) \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}\]
Using strategy rm
Applied clear-num0.5
\[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{k}}{{\left(\left(n \cdot 2\right) \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)}}}}\]
Final simplification0.5
\[\leadsto \frac{1}{\frac{\sqrt{k}}{{\left(\left(n \cdot 2\right) \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)}}}\]

herbie shell --seed 2018221 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))