1. **State the problem:** Simplify the expression $$\frac{16}{5m^2n} \times \frac{9ab^2}{10m^3n^3}$$. 2. **Rewrite the expression:** $$\frac{16}{5m^2n} \times \frac{9ab^2}{10m^3n^3} = \frac{16 \times 9ab^2}{5m^2n \times 10m^3n^3}$$ 3. **Multiply the numerators and denominators:** $$\frac{144ab^2}{50m^{2+3}n^{1+3}} = \frac{144ab^2}{50m^5n^4}$$ 4. **Simplify the coefficients:** $$\frac{144}{50} = \frac{72}{25}$$ (dividing numerator and denominator by 2) 5. **Write the simplified expression:** $$\frac{72ab^2}{25m^5n^4}$$ **Final answer:** $$\boxed{\frac{72ab^2}{25m^5n^4}}$$