Evaluate \( 6 u^{2} v^{3} \) when \( u=-\frac{2}{3} \) and \( v=-\frac{1}{2} \)

To evaluate the expression \( 6 u^{2} v^{3} \) with \( u = -\frac{2}{3} \) and \( v = -\frac{1}{2} \), follow these steps: 1. **Calculate \( u^2 \):** \[ u^2 = \left(-\frac{2}{3}\right)^2 = \frac{4}{9} \] 2. **Calculate \( v^3 \):** \[ v^3 = \left(-\frac{1}{2}\right)^3 = -\frac{1}{8} \] 3. **Multiply the results with the coefficient 6:** \[ 6 \times \frac{4}{9} \times \left(-\frac{1}{8}\right) = 6 \times \frac{4}{9} \times -\frac{1}{8} \] Simplify step-by-step: \[ 6 \times \frac{4}{9} = \frac{24}{9} = \frac{8}{3} \] \[ \frac{8}{3} \times -\frac{1}{8} = -\frac{8}{24} = -\frac{1}{3} \] So, the evaluated result is: \[ 6 u^{2} v^{3} = -\frac{1}{3} \] **Answer:** \(-\dfrac{1}{3}\)