1. **State the problem:** Simplify the expression $ (2u)^3 $ and write the answer without parentheses. 2. **Recall the power of a product rule:** For any numbers or variables $a$ and $b$, and a positive integer $n$, the rule states: $$ (ab)^n = a^n b^n $$ This means you raise each factor inside the parentheses to the power separately. 3. **Apply the rule:** $$ (2u)^3 = 2^3 \cdot u^3 $$ 4. **Calculate powers:** $$ 2^3 = 2 \times 2 \times 2 = 8 $$ 5. **Write the simplified expression:** $$ 8u^3 $$ **Final answer:** $8u^3$