$$ \left( \frac{1}{2} \right)^2 \cdot \left( 3\frac{1}{3} - 2\frac{8}{9} \right)^2 = \frac{1}{2^2} \cdot \left( \frac{3 \cdot 3 + 1}{3} - \frac{2 \cdot 9 + 8}{9} \right)^2 = \frac{1}{4} \cdot \left( \frac{10}{3} - \frac{26}{9} \right)^2 = \frac{1}{4} \cdot \left( \frac{10 \cdot 3}{3 \cdot 3} - \frac{26}{9} \right)^2 = \frac{1}{4} \cdot \left( \frac{30}{9} - \frac{26}{9} \right)^2 = \frac{1}{4} \cdot \left( \frac{4}{9} \right)^2 = \frac{1}{4} \cdot \frac{4^2}{9^2} = \frac{1}{4} \cdot \frac{16}{81} = \frac{16}{4 \cdot 81} = \frac{4}{81} $$
Ответ: $$\frac{4}{81}$$