1. **State the problem:** Simplify the expression $$\frac{18u^{14}}{3u^2} \times 10u^6$$. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$a^m \div a^n = a^{m-n}$$. - When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. - Multiply coefficients (numbers) normally. 3. **Simplify the fraction:** $$\frac{18u^{14}}{3u^2} = \frac{18}{3} \times u^{14-2} = 6u^{12}$$. 4. **Multiply by the remaining term:** $$6u^{12} \times 10u^6 = (6 \times 10) \times u^{12+6} = 60u^{18}$$. 5. **Final answer:** $$60u^{18}$$. This is the fully simplified form of the given expression.