Question: User: $(8^{-8})(8^{3})=$
1. **State the problem:** Simplify the expression $$(8^{-8})(8^{3})$$.
2. **Recall the exponent multiplication rule:** When multiplying powers with the same base, add the exponents:
$$a^{m} \times a^{n} = a^{m+n}$$
3. **Apply the rule:**
$$8^{-8} \times 8^{3} = 8^{-8+3}$$
4. **Simplify the exponent:**
$$-8 + 3 = -5$$
5. **Final expression:**
$$8^{-5}$$
6. **Interpretation:** A negative exponent means the reciprocal:
$$8^{-5} = \frac{1}{8^{5}}$$
**Final answer:**
$$\boxed{\frac{1}{8^{5}}}$$