1. **State the problem:** Simplify the expression $$9x^9 \div \left(\frac{x^3}{3}\right)$$. 2. **Rewrite the division by a fraction as multiplication:** Dividing by a fraction is the same as multiplying by its reciprocal. $$9x^9 \div \frac{x^3}{3} = 9x^9 \times \frac{3}{x^3}$$ 3. **Multiply the coefficients and variables:** $$9 \times 3 = 27$$ $$x^9 \times x^{-3} = x^{9-3} = x^6$$ So, $$9x^9 \times \frac{3}{x^3} = 27x^6$$ 4. **Final answer:** $$\boxed{27x^6}$$ --- **Additional expressions given:** (e) Simplify $$5t^5 \div 5t^5$$ $$= \frac{5t^5}{5t^5} = \cancel{5} \cancel{t^5} / \cancel{5} \cancel{t^5} = 1$$ (f) Simplify $$30b^5 \div 6b^1$$ $$= \frac{30b^5}{6b} = \frac{\cancel{30}^{5}b^5}{\cancel{6}^{1}b^1} = 5b^{5-1} = 5b^4$$ (g) Simplify $$4g^{20} \div 12g^{10}$$ $$= \frac{4g^{20}}{12g^{10}} = \frac{\cancel{4}^{1}g^{20}}{\cancel{12}^{3}g^{10}} = \frac{1}{3}g^{20-10} = \frac{1}{3}g^{10}$$ (h) Simplify $$7h^{11} \div 11h^7$$ $$= \frac{7h^{11}}{11h^7} = \frac{7}{11}h^{11-7} = \frac{7}{11}h^4$$