Answer
$\frac{5a^2}{b}.$
Work Step by Step
We divide by the monomial as follows:
$$
(15a^3b)\div(3ab^2)=\frac{15a^3b}{3ab^2}=\frac{5\cdot 3a^3b}{3ab^2}=\frac{5a^2}{b}.
$$
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