Initial program 0.3
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
Simplified0.3
\[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}\]
- Using strategy
rm Applied add-sqr-sqrt0.6
\[\leadsto \frac{{\color{blue}{\left(\sqrt{\ell} \cdot \sqrt{\ell}\right)}}^{\left(e^{w}\right)}}{e^{w}}\]
Applied unpow-prod-down0.6
\[\leadsto \frac{\color{blue}{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)} \cdot {\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}}{e^{w}}\]
- Using strategy
rm Applied add-cube-cbrt0.7
\[\leadsto \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)} \cdot {\left(\sqrt{\ell}\right)}^{\color{blue}{\left(\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right) \cdot \sqrt[3]{e^{w}}\right)}}}{e^{w}}\]
Applied pow-unpow0.7
\[\leadsto \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)} \cdot \color{blue}{{\left({\left(\sqrt{\ell}\right)}^{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right)}\right)}^{\left(\sqrt[3]{e^{w}}\right)}}}{e^{w}}\]
- Using strategy
rm Applied add-sqr-sqrt0.7
\[\leadsto \frac{{\left(\sqrt{\ell}\right)}^{\color{blue}{\left(\sqrt{e^{w}} \cdot \sqrt{e^{w}}\right)}} \cdot {\left({\left(\sqrt{\ell}\right)}^{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right)}\right)}^{\left(\sqrt[3]{e^{w}}\right)}}{e^{w}}\]
Applied pow-unpow0.7
\[\leadsto \frac{\color{blue}{{\left({\left(\sqrt{\ell}\right)}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left(\sqrt{e^{w}}\right)}} \cdot {\left({\left(\sqrt{\ell}\right)}^{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right)}\right)}^{\left(\sqrt[3]{e^{w}}\right)}}{e^{w}}\]
Final simplification0.7
\[\leadsto \frac{{\left({\left(\sqrt{\ell}\right)}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left(\sqrt{e^{w}}\right)} \cdot {\left({\left(\sqrt{\ell}\right)}^{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right)}\right)}^{\left(\sqrt[3]{e^{w}}\right)}}{e^{w}}\]
