$.[20$ Points$]$ Find a regular expression for each of the following languages.

$($a$)\{$ban

b

m : n $>=3,$ m $>=2\}.$

$($b$)\{$w in $\{$a$,$ b$\}$

$$

: every maximal substring of w consisting entirely of symbols a

is of length exactly $3\}.$

$($c$)\{$w in $\{$a$,$ b$\}$

$$

: w does not contain bab as a substring$\}.$

$($d$)\{$w in $\{$a$,$ b$\}$

$$

: w begins with bb and nb$($w$)$ mod $3=0\}.$