Initial program 2.1
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
Initial simplification2.0
\[\leadsto \frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\]
- Using strategy
rm Applied associate-/l*2.2
\[\leadsto \color{blue}{\frac{{k}^{m}}{\frac{1 + k \cdot \left(k + 10\right)}{a}}}\]
Taylor expanded around -inf 4.2
\[\leadsto \frac{{k}^{m}}{\color{blue}{\frac{1}{a} + \left(10 \cdot \frac{k}{a} + \frac{{k}^{2}}{a}\right)}}\]
Simplified0.3
\[\leadsto \frac{{k}^{m}}{\color{blue}{\frac{k}{a} \cdot \left(10 + k\right) + \frac{1}{a}}}\]
- Using strategy
rm Applied *-un-lft-identity0.3
\[\leadsto \frac{{k}^{m}}{\color{blue}{1 \cdot \left(\frac{k}{a} \cdot \left(10 + k\right) + \frac{1}{a}\right)}}\]
Applied add-cube-cbrt0.3
\[\leadsto \frac{\color{blue}{\left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right) \cdot \sqrt[3]{{k}^{m}}}}{1 \cdot \left(\frac{k}{a} \cdot \left(10 + k\right) + \frac{1}{a}\right)}\]
Applied times-frac0.3
\[\leadsto \color{blue}{\frac{\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}}{1} \cdot \frac{\sqrt[3]{{k}^{m}}}{\frac{k}{a} \cdot \left(10 + k\right) + \frac{1}{a}}}\]
Simplified0.3
\[\leadsto \color{blue}{\left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right)} \cdot \frac{\sqrt[3]{{k}^{m}}}{\frac{k}{a} \cdot \left(10 + k\right) + \frac{1}{a}}\]
Final simplification0.3
\[\leadsto \left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right) \cdot \frac{\sqrt[3]{{k}^{m}}}{\frac{1}{a} + \frac{k}{a} \cdot \left(k + 10\right)}\]
