Algebraic Problem Fractions

Question

Given the following fraction,

$$\frac{n}{2^{n-1}}(-2)^{n-1}$$

Is it correct that it simplifies to the following fraction,

$$(-1)^{n-1}n$$

I am in doubt because I have checked on three different places and they all gave different answer.

Answer 1

$\require{cancel}$

$$\frac{n}{2^{n-1}}(-2)^{n-1}=\frac{n}{\cancel{2^{n-1}}}(-1)^{n-1} \cdot \cancel{2^{n-1}}=n\cdot (-1)^{n-1},$$

so yes.