Compute each sum below. If applicable, write your answer as a fraction.

$(\frac{-1}{2})+(\frac{-1}{2}{)}^2+(\frac{-1}{2}{)}^3+$dots$+(\frac{-1}{2}{)}^8=$

${\displaystyle \underset{k=1}{\overset{9}{}}}5(4{)}^k=$