Question

Substituting the values, find $n$
$\frac{0.1}{0.2}={\left(\frac{10}{80}\right)}^{1/n}$ or ${\left(\frac{1}{2}\right)}^1={\left(\frac{1}{2}\right)}^{3/n}$

Answer 1

${\left(\frac{1}{2}\right)}^1={\left(\frac{1}{2}\right)}^{3/n}$
When bases are same, we can compare powers.
So, $\frac{1}{1}=\frac{3}{n}\Rightarrow n=3$