z transform property question I have a few questions about this assignment I am solving. 
It is q3.33(a) from oppenheim's DSP book 2nd edition. 

basically, the question gives you a pole zero plot, from which I was able to determine the correct x[n]. (Couple classmates confirmed my answer on that).

and it also gives you the y[n] of the form $(0.5)^n \cdot x[n]$. 

And wants you to work out a pole-zero of y[n] in the z plane.

my question is this: given that I already know X[z], can i just do z transform of $0.5^n$ as if it was $a^n \cdot u[n]$? 

Then I will have $[\frac{1}{1-0.5z^{-1}}] \cdot X[z]$ 

Thanks everyone.
HINT:

Use the property

$$z_0^nx[n]\Longleftrightarrow X(z/z_0)$$

with $z_0=1/2$. You can find this property in Table 3.2 on page 126. It's quite straightforward to show this property by using the definition of the $\mathcal{Z}$-transform.