Elementary Technical Mathematics

$$-\frac{3}{8}a^{7} b^{10}$$
By multiplying the numerical coefficients and adding the powers of the variables, we get $$\left(-\frac{5}{6} a^{2} b^{6}\right)\left(\frac{9}{20} a^{5} b^{4}\right)=-\frac{45}{120}a^{7} b^{10} =-\frac{9}{24}a^{7} b^{10}.$$ We can reduce the final fraction by $3$: $$=-\frac{3}{8}a^{7} b^{10}.$$