To simplify the expression $8^{-3} \cdot 8^{-5}$, use the rule for multiplying powers with the same base, which is to add the exponents:

$8^{-3} \cdot 8^{-5} = 8^{(-3) + (-5)} = 8^{-8}$

Thus, the simplified expression is $8^{-8}$.

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Here are 5 related questions to practice:

1. Simplify $5^{-2} \cdot 5^{-3}$.
2. Simplify $10^{-1} \cdot 10^{-4}$.
3. Simplify $2^{-5} \cdot 2^{-7}$.
4. Simplify $7^{-2} \cdot 7^{-6}$.
5. Simplify $3^{-4} \cdot 3^{-1}$.

Tip: When multiplying powers with the same base, always add the exponents, even if they are negative.