\(\frac{\frac{(e^{\varepsilon \cdot \left(a + b\right)} - 1)^*}{\frac{(e^{b \cdot \varepsilon} - 1)^*}{\varepsilon}}}{{\left(\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}\right)}^3}\)
- Started with
\[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
27.9
- Applied simplify to get
\[\color{red}{\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}} \leadsto \color{blue}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}}\]
12.3
- Using strategy
rm 12.3
- Applied add-cube-cbrt to get
\[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{\color{red}{(e^{a \cdot \varepsilon} - 1)^*}} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*} \leadsto \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{\color{blue}{{\left(\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}\right)}^3}} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}\]
12.4
- Applied add-cube-cbrt to get
\[\frac{\color{red}{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}}{{\left(\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}\right)}^3} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}\right)}^3}}{{\left(\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}\right)}^3} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}\]
12.4
- Applied cube-undiv to get
\[\color{red}{\frac{{\left(\sqrt[3]{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}\right)}^3}{{\left(\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}\right)}^3}} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*} \leadsto \color{blue}{{\left(\frac{\sqrt[3]{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}}{\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}}\right)}^3} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}\]
12.4
- Using strategy
rm 12.4
- Applied cube-div to get
\[\color{red}{{\left(\frac{\sqrt[3]{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}}{\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}}\right)}^3} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*} \leadsto \color{blue}{\frac{{\left(\sqrt[3]{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}\right)}^3}{{\left(\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}\right)}^3}} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}\]
12.4
- Applied associate-*l/ to get
\[\color{red}{\frac{{\left(\sqrt[3]{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}\right)}^3}{{\left(\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}\right)}^3} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}} \leadsto \color{blue}{\frac{{\left(\sqrt[3]{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}\right)}^3 \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}}{{\left(\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}\right)}^3}}\]
12.4
- Applied simplify to get
\[\frac{\color{red}{{\left(\sqrt[3]{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}\right)}^3 \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}}}{{\left(\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}\right)}^3} \leadsto \frac{\color{blue}{\frac{(e^{\varepsilon \cdot \left(a + b\right)} - 1)^*}{\frac{(e^{b \cdot \varepsilon} - 1)^*}{\varepsilon}}}}{{\left(\sqrt[3]{(e^{a \cdot \varepsilon} - 1)^*}\right)}^3}\]
12.4
