- Started with
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
1.1
- Applied simplify to get
\[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
9.0
- Using strategy
rm 9.0
- Applied div-inv to get
\[\left(\color{red}{\frac{x}{y}} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
9.0
- Applied associate-*l* to get
\[\color{red}{\left(\left(x \cdot \frac{1}{y}\right) \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\left(x \cdot \left(\frac{1}{y} \cdot {z}^{y}\right)\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
4.0
- Applied simplify to get
\[\left(x \cdot \color{red}{\left(\frac{1}{y} \cdot {z}^{y}\right)}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(x \cdot \color{blue}{\frac{{z}^{y}}{y}}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
3.9
- Using strategy
rm 3.9
- Applied pow-to-exp to get
\[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
4.5
- Applied div-exp to get
\[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
1.3
- Using strategy
rm 1.3
- Applied *-un-lft-identity to get
\[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot e^{\color{red}{\log a \cdot \left(t - 1.0\right) - b}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot e^{\color{blue}{1 \cdot \left(\log a \cdot \left(t - 1.0\right) - b\right)}}\]
1.3
- Applied exp-prod to get
\[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{red}{e^{1 \cdot \left(\log a \cdot \left(t - 1.0\right) - b\right)}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\log a \cdot \left(t - 1.0\right) - b\right)}}\]
1.4
- Applied simplify to get
\[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot {\color{red}{\left(e^{1}\right)}}^{\left(\log a \cdot \left(t - 1.0\right) - b\right)} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot {\color{blue}{e}}^{\left(\log a \cdot \left(t - 1.0\right) - b\right)}\]
1.4