Answer
$$\frac{4}{3}m^6n^8q^3 .$$
Work Step by Step
By multiplying the numerical coefficients and adding the powers of the variables, we get $$ \left(\frac{3}{5}m^4n^7\right)\left(\frac{20}{9}m^2nq^3\right)=\frac{20}{15}m^6n^8q^3=\frac{4}{3}m^6n^8q^3 .$$
