1. **State the problem:** Simplify the expression $(-2ab)^3$ with a positive exponent. 2. **Formula and rules:** When raising a product to a power, use the rule $$(xy)^n = x^n y^n$$ and for powers of a product with a negative sign, remember that $$(-x)^n = (-1)^n x^n$$. 3. **Apply the exponent to each factor:** $$(-2ab)^3 = (-1)^3 \times 2^3 \times a^3 \times b^3$$ 4. **Calculate each part:** - $(-1)^3 = -1$ because an odd power of -1 is -1. - $2^3 = 8$ - $a^3$ remains as is. - $b^3$ remains as is. 5. **Combine all parts:** $$(-2ab)^3 = -1 \times 8 \times a^3 \times b^3 = -8a^3b^3$$ 6. **Final answer:** $$\boxed{-8a^3b^3}$$