$11\mathrm{.}2-8$ Using only the fact that

$$

$$

$$

$[$

$$

$]$

$$

$$

$/$

$($

$$

$$

$$

$)$

and properties of the z$-$transform, find the z$-$transform of each of the following:

$($a$)$ n$2$u$[$n$]$

$($b$)$ n$2$nu$[$n$]$

$($c$)$ n$3$u$[$n$]$

$($d$)$ an$[$u$[$n$]$ u$[$n $$ m$]]$

$($e$)$ ne$2$nu$[$n $$ m$]$

$($f$)($n $2)(0\mathrm{.}5)$n $3$u$[$n $4]$