# Finding right quotient of $a^*b^*/b^*.$

I argue that right quotient of $$a^*b^*/b^*$$ is $$a^*$$,is that true?any help or argument to accept or reject my argument will be appreciated:)

$$a^*b^* / b^* = \{ w \ | \ \exists \ x, \ x \in b^* \land wx \in a^*b^*\} = a^*b^*$$. This is because $$wx \in a^*b^* \text{ AND } x \in b^*$$ means $$w$$ is of the form $$a^ib^j$$ for some $$i,j \in \mathbb{N} \cup \{0\}$$. Finish it off now.