Hey, can someone explain this to me?

Manhattan worked it like this but I think I am misunderstanding.

If 2^k - 2^k+1 + 2^k-1 = 2km, what is the value of m?

2^k(1-2^1+2^-1) = 2km

1-2^1+ 2^-1 = m

1-2+1/2 = m

-½ = m

My first step was the same as theirs to factor out the 2^k. However, I do not understand how they got (1-2^2+2^-1)

if I factored out 2^k how is there still a 2 left over for the second and 3rd value in the parenthesis?