use regular operations $\backslash$cup $,,*$

Let $\backslash$Sigma $=\{$a$,$ b$\}.$ Write regular expressions

for the languages below. In each case, simplify your expression as much as possible.$($a$)$ All strings in ${}^{**}$ with no more than three b$\text{'}$s$.$

$($b$)$ All strings in ${}^{**}$ with a number of $a\text{'}$s divisible by $3.$

$($c$)$ All strings in ${}^{**}$ that do not end with $aa.$

$($d$)$ All strings in ${}^{**}$ that do not have a substring $aa.$