Answer :

Solution :

Calculation:

Given that,$x\left(n\right)={\left(\frac{1}{2}\right)}^{n}1\left[n\right]$

Z Transform (ZT) of x(n) will be,

$x\left(z\right)=\frac{z}{z-\frac{1}{2}}=\frac{1}{1-\frac{1}{2}{z}^{-1}}$; ROC: $\left|z\right|>\frac{1}{2}$

And,$z\left(x\left(n-k\right)\right)=\frac{z^{-k}}{1-\frac{1}{2}{z}^{-1}}$ ; ROC:$\left|z\right|>\frac{1}{2}$