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

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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:** $$-\dfrac{1}{3}$$
The evaluated result is $$-\dfrac{1}{3}$$.

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

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