Given:
[tex]\frac{15a^{4}b^{3}}{12a^{2}b}[/tex]To find the quotient:
Let us write the given in the factored form.
[tex]\frac{15a^{4}b^{3}}{12a^{2}b}=\frac{3\times5\times a^4\times b^3}{3\times4\times a^2\times b}[/tex]On simplification we get,
[tex]\begin{gathered} =\frac{5}{4}a^{4-2}b^{3-1} \\ =\frac{5}{4}a^2b^2 \end{gathered}[/tex]Hence, the answer is,
[tex]\frac{5}{4}a^2b^2[/tex]