Question

How does 1^(-n) * (-1)^n simplify to (-1)^n?

Answer 1

well if you look at the 1st term

\[1^{-n} = \frac{1}{1^n}\]

this is always positive and is just 1


and

(-1)^n alternates between 1 and -1

so it becomes

\[1 \times (-1)^n\]

which is \[1 \times (-1)^n = (-1)^n \]