1. Problem: Simplify the expression $18x^6$ divided by $3x^2$. 2. Use the quotient rule for exponents: $\frac{a^m}{a^n}=a^{m-n}$, and divide the coefficients first. 3. Start with the numbers: $\frac{18}{3}=6$. 4. Show the division with cancellation: $$\frac{18x^6}{3x^2}=\frac{\cancel{18}x^6}{\cancel{3}x^2}=6\cdot \frac{x^6}{x^2}$$ 5. Apply the exponent rule: $$6\cdot \frac{x^6}{x^2}=6x^{6-2}=6x^4$$ 6. Final answer: $6x^4$.