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
\[\leadsto \frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(\frac{1}{2} - \frac{k}{2}\right)}}{\sqrt{k}}\]
- Using strategy
rm Applied *-un-lft-identity0.4
\[\leadsto \frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(\frac{1}{2} - \frac{k}{2}\right)}}{\color{blue}{1 \cdot \sqrt{k}}}\]
Applied sub-neg0.4
\[\leadsto \frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\color{blue}{\left(\frac{1}{2} + \left(-\frac{k}{2}\right)\right)}}}{1 \cdot \sqrt{k}}\]
Applied unpow-prod-up0.4
\[\leadsto \frac{\color{blue}{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\frac{1}{2}} \cdot {\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(-\frac{k}{2}\right)}}}{1 \cdot \sqrt{k}}\]
Applied times-frac0.5
\[\leadsto \color{blue}{\frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\frac{1}{2}}}{1} \cdot \frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(-\frac{k}{2}\right)}}{\sqrt{k}}}\]
Simplified0.5
\[\leadsto \color{blue}{\sqrt{\left(\pi \cdot 2\right) \cdot n}} \cdot \frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(-\frac{k}{2}\right)}}{\sqrt{k}}\]
Final simplification0.5
\[\leadsto \sqrt{\left(\pi \cdot 2\right) \cdot n} \cdot \frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(-\frac{k}{2}\right)}}{\sqrt{k}}\]
