1. **State the problem:** Simplify the expression $$(-8)^{-\frac{1}{3}}$$ and express the answer with positive exponents. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ and rational exponent $n$, $$a^{-n} = \frac{1}{a^n}$$. 3. **Apply the negative exponent rule:** $$(-8)^{-\frac{1}{3}} = \frac{1}{(-8)^{\frac{1}{3}}}$$ 4. **Evaluate the cube root:** The cube root of $-8$ is $-2$ because $$(-2)^3 = -8$$. 5. **Substitute the cube root value:** $$\frac{1}{(-8)^{\frac{1}{3}}} = \frac{1}{-2} = -\frac{1}{2}$$ 6. **Final answer:** $$(-8)^{-\frac{1}{3}} = -\frac{1}{2}$$