if n < -4.5062436167830026e+18 or 2.946896988150068e+20 < n

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   60.5
2. Using strategy rm
   60.5
3. Applied add-exp-log to get
   \[{\color{red}{\left(x + 1\right)}}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)} \leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   60.5
4. Applied pow-exp to get
   \[\color{red}{{\left(e^{\log \left(x + 1\right)}\right)}^{\left(\frac{1}{n}\right)}} - {x}^{\left(\frac{1}{n}\right)} \leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{n}}} - {x}^{\left(\frac{1}{n}\right)}\]
   60.5
5. Applied simplify to get
   \[e^{\color{red}{\log \left(x + 1\right) \cdot \frac{1}{n}}} - {x}^{\left(\frac{1}{n}\right)} \leadsto e^{\color{blue}{\frac{\log_* (1 + x)}{n}}} - {x}^{\left(\frac{1}{n}\right)}\]
   60.5
6. Applied taylor to get
   \[e^{\frac{\log_* (1 + x)}{n}} - {x}^{\left(\frac{1}{n}\right)} \leadsto \left(\frac{\log_* (1 + \frac{1}{x})}{n} + \left(1 + \frac{1}{2} \cdot \frac{{\left(\log_* (1 + \frac{1}{x})\right)}^2}{{n}^2}\right)\right) - {x}^{\left(\frac{1}{n}\right)}\]
   60.5
7. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{\log_* (1 + \frac{1}{x})}{n} + \left(1 + \frac{1}{2} \cdot \frac{{\left(\log_* (1 + \frac{1}{x})\right)}^2}{{n}^2}\right)\right)} - {x}^{\left(\frac{1}{n}\right)} \leadsto \color{blue}{\left(\frac{\log_* (1 + \frac{1}{x})}{n} + \left(1 + \frac{1}{2} \cdot \frac{{\left(\log_* (1 + \frac{1}{x})\right)}^2}{{n}^2}\right)\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   60.5
8. Applied simplify to get
   \[\color{red}{\left(\frac{\log_* (1 + \frac{1}{x})}{n} + \left(1 + \frac{1}{2} \cdot \frac{{\left(\log_* (1 + \frac{1}{x})\right)}^2}{{n}^2}\right)\right) - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{(\left(\frac{\log_* (1 + \frac{1}{x})}{n}\right) * \left((\left(\frac{\log_* (1 + \frac{1}{x})}{n}\right) * \frac{1}{2} + 1)_*\right) + \left(1 - {x}^{\left(\frac{1}{n}\right)}\right))_*}\]
   56.4

if -4.5062436167830026e+18 < n < 2.946896988150068e+20

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   6.8
2. Using strategy rm
   6.8
3. Applied add-exp-log to get
   \[{\color{red}{\left(x + 1\right)}}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)} \leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   6.8
4. Applied pow-exp to get
   \[\color{red}{{\left(e^{\log \left(x + 1\right)}\right)}^{\left(\frac{1}{n}\right)}} - {x}^{\left(\frac{1}{n}\right)} \leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{n}}} - {x}^{\left(\frac{1}{n}\right)}\]
   6.8
5. Applied simplify to get
   \[e^{\color{red}{\log \left(x + 1\right) \cdot \frac{1}{n}}} - {x}^{\left(\frac{1}{n}\right)} \leadsto e^{\color{blue}{\frac{\log_* (1 + x)}{n}}} - {x}^{\left(\frac{1}{n}\right)}\]
   5.9