1. **State the problem:** Simplify the expression $$12a^5 b^3 \div 9a^3 b^5$$. 2. **Write the division as a fraction:** $$\frac{12a^5 b^3}{9a^3 b^5}$$ 3. **Simplify the coefficients:** $$\frac{\cancel{12}^{4} \times a^5 b^3}{\cancel{9}^{3} \times a^3 b^5} = \frac{4a^5 b^3}{3a^3 b^5}$$ 4. **Apply the quotient rule for exponents:** For the same base, subtract exponents when dividing: $$a^{5-3} = a^2$$ $$b^{3-5} = b^{-2}$$ 5. **Rewrite the expression with simplified exponents:** $$\frac{4a^2 b^{-2}}{3} = \frac{4a^2}{3b^2}$$ 6. **Final simplified expression:** $$\frac{4a^2}{3b^2}$$ This means the original expression simplifies to $$\frac{4a^2}{3b^2}$$.