(28) \( \frac{4 m^{3}}{30 n} \div \frac{20 m^{6}}{3 n^{5}} \)

To solve \( \frac{4 m^{3}}{30 n} \div \frac{20 m^{6}}{3 n^{5}} \), we first rewrite the division as multiplication by the reciprocal: \[ \frac{4 m^{3}}{30 n} \times \frac{3 n^{5}}{20 m^{6}}. \] Now, multiply the numerators and the denominators: \[ \frac{4 m^{3} \cdot 3 n^{5}}{30 n \cdot 20 m^{6}} = \frac{12 m^{3} n^{5}}{600 n m^{6}}. \] Next, simplify the fraction. The greatest common divisor of 12 and 600 is 12. Divide both the numerator and denominator by 12: \[ \frac{1 m^{3} n^{5}}{50 n m^{6}} = \frac{n^{5}}{50 n} \cdot \frac{m^{3}}{m^{6}}. \] Now, simplify each part: \[ \frac{n^{5}}{n} = n^{4}, \quad \text{and} \quad \frac{m^{3}}{m^{6}} = \frac{1}{m^{3}}. \] Thus, we can combine the results: \[ \frac{n^{4}}{50 m^{3}}. \] The final simplified result is: \[ \frac{n^{4}}{50 m^{3}}. \]