# 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? ## 2 Answers

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.

No you have done a small mistake how a^-n became a^n? So it is like this the ROC is right sided • Please, use the formatting options provided by the site to write your answer instead of posting images. – Tendero Mar 19 '17 at 14:35
• I don't know how to do such things – Ch.Siva Ram Kishore Mar 19 '17 at 14:37
• You can check out how to improve your formatting here. – Tendero Mar 19 '17 at 15:02
• Moni alfarsia if you put your question as answered then it is better – Ch.Siva Ram Kishore Mar 19 '17 at 15:20
• Ok , Iam sorry but Its my first time that I have post in this website , In second time make sure that I will not post a picture . – moni alfarsia Mar 19 '17 at 15:49