Thanks for rewriting this. It's nice to be able to read the question clearly.
44b^5 = 2 * 2 * 11 * b * b * b * b * b
36b = 2 * 2 * 3 * 3 * b
There are two 2s that each of them have.
There is one b that each of them have.
Greatest common factor = 2 * 2 * b
4b <<<< answer