(6,75-4,5•1 2/3)•(-1 1/3)3

To solve the expression \( (6.75 - 4.5 \cdot 1 \frac{2}{3}) \cdot (-1 \frac{1}{3})^3 \), we can follow these steps:

1. Convert mixed and fractional numbers to improper fractions:

   • \( 1 \frac{2}{3} = \frac{5}{3} \)
   • \( -1 \frac{1}{3} = -\frac{4}{3} \)

2. Calculate \( 4.5 \cdot 1 \frac{2}{3} \): \[ 4.5 \cdot \frac{5}{3} = \frac{4.5 \cdot 5}{3} = \frac{22.5}{3} = 7.5 \]

3. Substitute back into the expression: \[ (6.75 - 7.5) \cdot (-\frac{4}{3})^3 \]

4. Calculate \( 6.75 - 7.5 \): \[ 6.75 - 7.5 = -0.75 \]

5. Calculate \( (-\frac{4}{3})^3 \): \[ (-\frac{4}{3})^3 = -\frac{4^3}{3^3} = -\frac{64}{27} \]

6. Combine the results: \[ -0.75 \cdot -\frac{64}{27} \] Convert \(-0.75\) to a fraction: \[ -0.75 = -\frac{3}{4} \]

7. Multiply the fractions: \[ -\frac{3}{4} \cdot -\frac{64}{27} = \frac{3 \cdot 64}{4 \cdot 27} = \frac{192}{108} = \frac{16}{9} \quad (\text{after simplification}) \]

So, the final answer is: \[ \frac{16}{9} \]