Removing part of an exponent

Question

I have come across a statement in my textbook which I do not understand and have searched online for an answer but this specific case does not seem to come up $x_{n}=(\frac{1}{2})^{n-1}$ can be rearranged to $x_{n}=2(\frac{1}{2})^{n}$. I am not sure how you remove only part of the exponent. Is there a general rule for removing part of an exponent that works in any expression?

Answer 1

$$\left(\frac12\right)^{n-1}\times\frac12\times2=\left(\frac12\right)^n\times2$$