1. **State the problem:** Simplify the expression $u(u^2)$ and write the answer with only positive exponents. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$ 3. **Apply the rule:** Here, the base is $u$, so: $$u \times u^2 = u^{1+2}$$ 4. **Simplify the exponent:** $$u^{1+2} = u^3$$ 5. **Final answer:** The simplified expression with positive exponents is: $$u^3$$