Question: Evaluate.
$$\left(-\frac{2}{3}\right)^3 \cdot \frac{1}{2}$$
1. **State the problem:** Evaluate $$\left(-\frac{2}{3}\right)^3 \cdot \frac{1}{2}$$ and simplify the answer.
2. **Recall the formula:** When raising a fraction to a power, raise both numerator and denominator to that power: $$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$.
3. **Calculate the cube:**
$$\left(-\frac{2}{3}\right)^3 = \frac{(-2)^3}{3^3} = \frac{-8}{27}$$
4. **Multiply by $$\frac{1}{2}$$:**
$$\frac{-8}{27} \cdot \frac{1}{2} = \frac{-8 \cdot 1}{27 \cdot 2} = \frac{-8}{54}$$
5. **Simplify the fraction:**
$$\frac{-8}{54} = \frac{\cancel{-8}^{-4 \times 2}}{\cancel{54}^{27 \times 2}} = \frac{-4}{27}$$
6. **Final answer:**
$$\boxed{-\frac{4}{27}}$$