a) \( \left(\frac{3}{5} m n^{2}-\frac{9 m}{2}\right)\left(\frac{6}{5} m^{3} n^{2}+\frac{3}{2} n\right)=\frac{18 m^{\square} n^{4}}{25}-\frac{27 m^{4} n^{\square}}{5}+\frac{9 m n^{\square}}{10}+2 \) b) \( \left(-6 m n^{\square} n^{3}-7 m^{\square}\right)\left(5 m^{\square}+2 n-2\right)=-30 m^{6} n^{3}-12 m^{2} n^{5}+12 m^{2} n^{3}-35 m \) \( -14 m^{3} n^{2}+14 m^{3} \) c) \( 0.5 m n\left(-2.5 m^{2}+1,5 m^{3} n-9\right)=-1,25 m^{\square} n^{\square}+0.75 m^{\square} n^{\square}-4.5 m \)

To solve the problems, we need to expand the expressions and match the coefficients to find the missing exponents represented by the squares. ### Part a We need to expand: \[ \left(\frac{3}{5} m n^{2}-\frac{9 m}{2}\right)\left(\frac{6}{5} m^{3} n^{2}+\frac{3}{2} n\right) \] 1. **First Term**: \[ \frac{3}{5} m n^{2} \cdot \frac{6}{5} m^{3} n^{2} = \frac{18}{25} m^{4} n^{4} \] 2. **Second Term**: \[ \frac{3}{5} m n^{2} \cdot \frac{3}{2} n = \frac{9}{10} m n^{3} \] 3. **Third Term**: \[ -\frac{9 m}{2} \cdot \frac{6}{5} m^{3} n^{2} = -\frac{54}{10} m^{4} n^{2} = -\frac{27}{5} m^{4} n^{2} \] 4. **Fourth Term**: \[ -\frac{9 m}{2} \cdot \frac{3}{2} n = -\frac{27}{4} m n \] Combining these results: \[ \frac{18}{25} m^{4} n^{4} + \frac{9}{10} m n^{3} - \frac{27}{5} m^{4} n^{2} - \frac{27}{4} m n \] Now, we can match the coefficients with the given expression: \[ \frac{18 m^{\square} n^{4}}{25} - \frac{27 m^{4} n^{\square}}{5} + \frac{9 m n^{\square}}{10} + 2 \] From the expansion: - \( m^{\square} = 4 \) (since \( m^{4} \)) - \( n^{\square} = 2 \) (since \( n^{2} \)) - \( n^{\square} = 3 \) (since \( n^{3} \)) ### Part b We need to expand: \[ \left(-6 m n^{\square} n^{3}-7 m^{\square}\right)\left(5 m^{\square}+2 n-2\right) \] 1. **First Term**: \[ -6 m n^{\square} n^{3} \cdot 5 m^{\square} = -30 m^{\square + 1} n^{\square + 3} \] 2. **Second Term**: \[ -6 m n^{\square} n^{3} \cdot 2 n = -12 m n^{\square + 4} \] 3. **Third Term**: \[ -6 m n^{\square} n^{3} \cdot -2 = 12 m n^{\square + 3} \] 4. **Fourth Term**: \[ -7 m^{\square} \cdot 5 m^{\square} = -35 m^{2\square} \] 5. **Fifth Term**: \[ -7 m^{\square} \cdot 2 n = -14 m^{\square} n \] 6. **Sixth Term**: \[ -7 m^{\square} \cdot -2 = 14 m^{\square} \] Combining these results: \[ -30 m^{\square + 1} n^{\square + 3} - 12 m n^{\square + 4} + 12 m n^{\square + 3} - 35 m^{2\square} - 14 m^{\square} n + 14 m^{\square} \] Now, we can match the coefficients with the given expression: \[ -30 m^{6} n^{3} - 12 m^{2} n^{5} + 12 m^{2} n^{3} - 35 m - 14 m^{3} n^{2} + 14 m^{3} \] From the expansion: - \( n^{\square} = 3 \) (since \(