Answer
$\frac{a^{3}b^{5}}{3}$
Work Step by Step
Based on the quotient rule for exponents, we know that $\frac{a^{m}}{{a}^{n}}=a^{m-n}, a\ne0$ (where $m$ and $n$ are positive integers and $a$ is a real number).
Therefore, $\frac{9a^{4}b^{7}}{27ab^{2}}=\frac{9}{27}\times a^{4-1}\times b^{7-2}=\frac{1}{3}\times a^{3}\times b^{5}=\frac{a^{3}b^{5}}{3}$.