Initial program 2.1
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
Initial simplification2.1
\[\leadsto \frac{{k}^{m} \cdot a}{(k \cdot \left(k + 10\right) + 1)_*}\]
- Using strategy
rm Applied associate-/l*2.2
\[\leadsto \color{blue}{\frac{{k}^{m}}{\frac{(k \cdot \left(k + 10\right) + 1)_*}{a}}}\]
Taylor expanded around -inf 4.1
\[\leadsto \frac{{k}^{m}}{\color{blue}{\frac{1}{a} + \left(10 \cdot \frac{k}{a} + \frac{{k}^{2}}{a}\right)}}\]
Simplified2.1
\[\leadsto \frac{{k}^{m}}{\color{blue}{(10 \cdot \left(\frac{k}{a}\right) + \left((\left(\frac{k}{a}\right) \cdot k + \left(\frac{1}{a}\right))_*\right))_*}}\]
- Using strategy
rm Applied add-cube-cbrt2.6
\[\leadsto \frac{{k}^{m}}{\color{blue}{\left(\sqrt[3]{(10 \cdot \left(\frac{k}{a}\right) + \left((\left(\frac{k}{a}\right) \cdot k + \left(\frac{1}{a}\right))_*\right))_*} \cdot \sqrt[3]{(10 \cdot \left(\frac{k}{a}\right) + \left((\left(\frac{k}{a}\right) \cdot k + \left(\frac{1}{a}\right))_*\right))_*}\right) \cdot \sqrt[3]{(10 \cdot \left(\frac{k}{a}\right) + \left((\left(\frac{k}{a}\right) \cdot k + \left(\frac{1}{a}\right))_*\right))_*}}}\]
Applied *-un-lft-identity2.6
\[\leadsto \frac{\color{blue}{1 \cdot {k}^{m}}}{\left(\sqrt[3]{(10 \cdot \left(\frac{k}{a}\right) + \left((\left(\frac{k}{a}\right) \cdot k + \left(\frac{1}{a}\right))_*\right))_*} \cdot \sqrt[3]{(10 \cdot \left(\frac{k}{a}\right) + \left((\left(\frac{k}{a}\right) \cdot k + \left(\frac{1}{a}\right))_*\right))_*}\right) \cdot \sqrt[3]{(10 \cdot \left(\frac{k}{a}\right) + \left((\left(\frac{k}{a}\right) \cdot k + \left(\frac{1}{a}\right))_*\right))_*}}\]
Applied times-frac2.6
\[\leadsto \color{blue}{\frac{1}{\sqrt[3]{(10 \cdot \left(\frac{k}{a}\right) + \left((\left(\frac{k}{a}\right) \cdot k + \left(\frac{1}{a}\right))_*\right))_*} \cdot \sqrt[3]{(10 \cdot \left(\frac{k}{a}\right) + \left((\left(\frac{k}{a}\right) \cdot k + \left(\frac{1}{a}\right))_*\right))_*}} \cdot \frac{{k}^{m}}{\sqrt[3]{(10 \cdot \left(\frac{k}{a}\right) + \left((\left(\frac{k}{a}\right) \cdot k + \left(\frac{1}{a}\right))_*\right))_*}}}\]
Simplified2.6
\[\leadsto \color{blue}{\frac{1}{\sqrt[3]{(\left(10 + k\right) \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*} \cdot \sqrt[3]{(\left(10 + k\right) \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*}}} \cdot \frac{{k}^{m}}{\sqrt[3]{(10 \cdot \left(\frac{k}{a}\right) + \left((\left(\frac{k}{a}\right) \cdot k + \left(\frac{1}{a}\right))_*\right))_*}}\]
Simplified0.7
\[\leadsto \frac{1}{\sqrt[3]{(\left(10 + k\right) \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*} \cdot \sqrt[3]{(\left(10 + k\right) \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*}} \cdot \color{blue}{\frac{{k}^{m}}{\sqrt[3]{(\left(\frac{k}{a}\right) \cdot \left(10 + k\right) + \left(\frac{1}{a}\right))_*}}}\]
Final simplification0.7
\[\leadsto \frac{1}{\sqrt[3]{(\left(10 + k\right) \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*} \cdot \sqrt[3]{(\left(10 + k\right) \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*}} \cdot \frac{{k}^{m}}{\sqrt[3]{(\left(\frac{k}{a}\right) \cdot \left(10 + k\right) + \left(\frac{1}{a}\right))_*}}\]
