Given \[x[n]=a^nu[n]\], find the Z-transform and ROC of \[b^{2(n+1)}x[n/5]\].
I know that the Z-transform of \[x[n]=a^nu[n] \leftrightarrow \frac{1}{1-az^{-1} \] and the ROC is \[|z|>|a|\].
I was thinking of setting \[f[n]=b^{2(n+1)}\] and \[g[n]=[n/5]\] then calculate the Z-transform of \[f[n]g[n]\]. I wasn't sure of the property for this as compared to f[n]*g[n] <-> F(z)G(z).
If I were to do that then I was thinking of using the formal definition of the Z-transform for \[b^{2(n+1)}\] and I wouldn't be sure how to calculate that.
The way I'm thinking seems arduous and to be the long route of doing this.