1. **State the problem:** Evaluate the expression $$(-8)^{-2} \times 3^{-4}$$. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ and integer $n$, $$a^{-n} = \frac{1}{a^n}$$. 3. **Apply the rule to each term:** $$(-8)^{-2} = \frac{1}{(-8)^2}$$ $$3^{-4} = \frac{1}{3^4}$$ 4. **Calculate the powers:** $$(-8)^2 = (-8) \times (-8) = 64$$ $$3^4 = 3 \times 3 \times 3 \times 3 = 81$$ 5. **Rewrite the expression:** $$(-8)^{-2} \times 3^{-4} = \frac{1}{64} \times \frac{1}{81}$$ 6. **Multiply the fractions:** $$\frac{1}{64} \times \frac{1}{81} = \frac{1}{64 \times 81}$$ 7. **Calculate the denominator:** $$64 \times 81 = 5184$$ 8. **Final answer:** $$\boxed{\frac{1}{5184}}$$