1. First, state the problem: evaluate $8^3 \times 4^{-2}$. 2. Calculate $8^3$: since $8 = 2^3$, then $8^3 = (2^3)^3 = 2^{9} = 512$. 3. Calculate $4^{-2}$: since $4 = 2^2$, then $4^{-2} = (2^2)^{-2} = 2^{-4} = \frac{1}{2^4} = \frac{1}{16}$. 4. Multiply the results: $512 \times \frac{1}{16} = \frac{512}{16} = 32$. 5. Therefore, the answer is $32$.