1. **State the problem:** We need to find an expression equivalent to $8^{-2}$. 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:** $$8^{-2} = \frac{1}{8^2}$$ 4. **Calculate $8^2$:** $$8^2 = 8 \times 8 = 64$$ 5. **Substitute back:** $$8^{-2} = \frac{1}{64}$$ 6. **Conclusion:** The expression equivalent to $8^{-2}$ is $\frac{1}{64}$.