1. **State the problem:** We want to find an expression equivalent to $$5^8 \cdot 5^{-10}$$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Apply the rule:** $$5^8 \cdot 5^{-10} = 5^{8 + (-10)} = 5^{-2}$$ 4. **Rewrite negative exponent:** A negative exponent means the reciprocal: $$5^{-2} = \frac{1}{5^2}$$ 5. **Final answer:** $$5^8 \cdot 5^{-10} = \frac{1}{5^2}$$ This matches the option **1 / 5^2**.