Find the $\mathcal Z$-transform of this function? I need to find the $\mathcal Z$-transform of $x(n)=a^{-n} u(n)$. Assume, $a$ is a positive constant , but the power of $a$ is negative. 

Looking at the transform table, I found that $\mathcal Z$-transform for $x(n)=a^{-n} u(n)$ is not there, so I tried to found it by on my own, but I am not sure if my answer is right, please can anyone check it and correct me, in case?
Doing some calculations is appreciated. However, it is preferred that you write them in the question because a picture can vanish more easily. Do not hesitate to edit the math.

To help you with an hint in checking your answer, remember that:

$$ a^{-n} = \left(\frac{1}{a}\right)^n$$

a standard trick to play with known tables.