1. **Problem 1:** Simplify the expression $$\frac{2x^4 y^{-4} z^{-3}}{3x^2 y^{-3} z^4}$$. 2. Use the quotient rule for exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. Apply the rule to each variable: $$\frac{2}{3} \times x^{4-2} \times y^{-4 - (-3)} \times z^{-3 - 4} = \frac{2}{3} x^2 y^{-1} z^{-7}$$. 4. Rewrite negative exponents as positive by moving terms to denominator: $$\frac{2}{3} x^2 \times \frac{1}{y} \times \frac{1}{z^7} = \frac{2x^2}{3yz^7}$$. 5. **Problem 2:** Simplify $$\left(2x^4 y^{-3}\right)^{-1}$$. 6. Use the power of a product rule: $$\left(a^m b^n\right)^p = a^{mp} b^{np}$$. 7. Apply the negative exponent: $$2^{-1} x^{4 \times (-1)} y^{-3 \times (-1)} = \frac{1}{2} x^{-4} y^3$$. 8. Rewrite negative exponent: $$\frac{1}{2} \times \frac{y^3}{x^4} = \frac{y^3}{2x^4}$$. **Final answers:** 1. $$\frac{2x^2}{3yz^7}$$ 2. $$\frac{y^3}{2x^4}$$