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 pow-sub0.4
\[\leadsto \frac{\color{blue}{\frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\frac{1}{2}}}{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(\frac{k}{2}\right)}}}}{\sqrt{k}}\]
Applied associate-/l/0.4
\[\leadsto \color{blue}{\frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\frac{1}{2}}}{\sqrt{k} \cdot {\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(\frac{k}{2}\right)}}}\]
Simplified0.4
\[\leadsto \frac{\color{blue}{\sqrt{\left(2 \cdot n\right) \cdot \pi}}}{\sqrt{k} \cdot {\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(\frac{k}{2}\right)}}\]
- Using strategy
rm Applied clear-num0.4
\[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{k} \cdot {\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(\frac{k}{2}\right)}}{\sqrt{\left(2 \cdot n\right) \cdot \pi}}}}\]
- Using strategy
rm Applied *-un-lft-identity0.4
\[\leadsto \frac{1}{\frac{\sqrt{k} \cdot {\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(\frac{k}{2}\right)}}{\color{blue}{1 \cdot \sqrt{\left(2 \cdot n\right) \cdot \pi}}}}\]
Applied times-frac0.5
\[\leadsto \frac{1}{\color{blue}{\frac{\sqrt{k}}{1} \cdot \frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(\frac{k}{2}\right)}}{\sqrt{\left(2 \cdot n\right) \cdot \pi}}}}\]
Simplified0.5
\[\leadsto \frac{1}{\color{blue}{\sqrt{k}} \cdot \frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(\frac{k}{2}\right)}}{\sqrt{\left(2 \cdot n\right) \cdot \pi}}}\]
Final simplification0.5
\[\leadsto \frac{1}{\sqrt{k} \cdot \frac{{\left(\left(n \cdot 2\right) \cdot \pi\right)}^{\left(\frac{k}{2}\right)}}{\sqrt{\left(n \cdot 2\right) \cdot \pi}}}\]
