1. **State the problem:** Simplify the expression $$\left( \frac{\left( \frac{5}{3} \right)^{-2} \cdot \left( \frac{5}{3} \right)^{-3}}{\left( \frac{5}{3} \right)^{-1}} \right)^{-4}$$. 2. **Recall the exponent rules:** - When multiplying powers with the same base, add exponents: $$a^m \cdot a^n = a^{m+n}$$. - When dividing powers with the same base, subtract exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - When raising a power to another power, multiply exponents: $$(a^m)^n = a^{m \cdot n}$$. 3. **Simplify inside the parentheses:** $$\left( \frac{\left( \frac{5}{3} \right)^{-2} \cdot \left( \frac{5}{3} \right)^{-3}}{\left( \frac{5}{3} \right)^{-1}} \right) = \left( \frac{5}{3} \right)^{-2 + (-3) - (-1)} = \left( \frac{5}{3} \right)^{-2 - 3 + 1} = \left( \frac{5}{3} \right)^{-4}$$ 4. **Apply the outer exponent:** $$\left( \left( \frac{5}{3} \right)^{-4} \right)^{-4} = \left( \frac{5}{3} \right)^{-4 \times (-4)} = \left( \frac{5}{3} \right)^{16}$$ 5. **Final answer:** $$\boxed{\left( \frac{5}{3} \right)^{16}}$$