\(\left(-\frac{7}{3}\right)^{3} \cdot \left(\frac{9}{7}\right)^{2} = -\frac{7^{3}}{3^{3}} \cdot \frac{9^{2}}{7^{2}} = -\frac{7^{3}}{3^{3}} \cdot \frac{(3^{2})^{2}}{7^{2}} = -\frac{7^{3}}{3^{3}} \cdot \frac{3^{4}}{7^{2}} = -7^{3-2} \cdot 3^{4-3} = -7 \cdot 3 = -21\)