1. **State the problem:** Simplify the expression $$\frac{20a^3}{45a}$$. 2. **Recall the formula and rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify the coefficients:** $$\frac{20}{45} = \frac{\cancel{5} \times 4}{\cancel{5} \times 9} = \frac{4}{9}$$. 4. **Simplify the variables:** $$\frac{a^3}{a} = a^{3-1} = a^2$$. 5. **Combine the results:** $$\frac{20a^3}{45a} = \frac{4}{9} a^2$$. **Final answer:** $$\frac{4}{9} a^2$$