What is the regular expression to the given language? I can't really find out, how can the following given Language be written down with regular expressions

$
L = \{ a^{3k-1} b^n a^{2t} \mid n &gt; 0; k, t\ge1 \}
$

I had some guesses, but I don't know how to express the part $a^{3k-1}$ of the Language.
Probably it should look something like this:

$(aaa)^+$ [something] $b^*(aa^+)$
Look at the three parts of your language:


For the $a^{3k-1}$ part, we have possibilities $a^2, a^5, a^8, \dots$. For this part we'll have any 2 $a$s plus a multiple of 3 $a$s. That's expressible as $aa(aaa)^*$.
The $b^n$ part is easy, it's just $b^+$, since you need $n&gt;0$.
The $a^{2t}$ part is likewise easy. Since $t\ge 1$ we can express this as $(aa)^+$.


Now concatenate these three regular expressions.