1. **State the problem:** Simplify the expression $$\frac{16 a^8 b^4}{8 a^3 b^2}$$. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$\frac{x^m}{x^n} = x^{m-n}$$. - Simplify coefficients by dividing them. 3. **Simplify the coefficients:** $$\frac{16}{8} = \cancel{\frac{16}{8}} = 2$$ 4. **Simplify the powers of $a$:** $$\frac{a^8}{a^3} = a^{8-3} = a^5$$ 5. **Simplify the powers of $b$:** $$\frac{b^4}{b^2} = b^{4-2} = b^2$$ 6. **Combine all simplified parts:** $$2 a^5 b^2$$ **Final answer:** $$2 a^5 b^2$$