1. **State the problem:** Simplify and evaluate the expression $$\left(3^3 - \frac{1}{5^{-2}}\right)^{-4}$$. 2. **Recall the rules:** - Exponentiation: $a^b$ means $a$ raised to the power $b$. - Negative exponents: $a^{-n} = \frac{1}{a^n}$. - Order of operations: Evaluate exponents first, then multiplication/division, then addition/subtraction. 3. **Evaluate inside the parentheses:** - Calculate $3^3 = 27$. - Calculate $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$. - Then $\frac{1}{5^{-2}} = \frac{1}{\frac{1}{25}} = 25$. 4. **Simplify inside the parentheses:** $$27 - 25 = 2$$ 5. **Apply the outer exponent:** $$2^{-4} = \frac{1}{2^4} = \frac{1}{16}$$ **Final answer:** $$\frac{1}{16}$$