Answer
$-\frac{5}{21}a^5b^6+\frac{1}{3}a^3b^5+\frac{25}{48}a^2b^8.$
Work Step by Step
We multiply each term of the polynomial by the monomial and then add the products as follows
$$
-\frac{5}{9} a^2 b^{4}\left(\frac{3}{7} a^{3}b^2-\frac{3}{5} a b -\frac{15}{16} b^{4}\right)=-\frac{5}{21}a^5b^6+\frac{1}{3}a^3b^5+\frac{25}{48}a^2b^8.
$$
