1. **State the problem:** Simplify the expression $$\frac{18u^{14}}{3u^2 \times 10u^6}$$. 2. **Write the expression clearly:** $$\frac{18u^{14}}{3u^2 \times 10u^6} = \frac{18u^{14}}{30u^{2+6}}$$ because when multiplying powers with the same base, add the exponents. 3. **Simplify the denominator:** $$30u^{8}$$. 4. **Divide the coefficients:** $$\frac{18}{30} = \frac{3}{5}$$ after dividing numerator and denominator by 6. 5. **Subtract the exponents of $u$ in numerator and denominator:** $$u^{14-8} = u^{6}$$. 6. **Write the simplified expression:** $$\frac{3}{5}u^{6}$$. **Final answer:** $$\frac{3}{5}u^{6}$$. This means the original expression simplifies to three-fifths times $u$ to the sixth power.