1. **State the problem:** Simplify the expression $\frac{b^{-2}}{b^{6}}$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same base, subtract the exponents: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$ 3. **Apply the rule:** Here, the base is $b$, so $$\frac{b^{-2}}{b^{6}} = b^{-2 - 6}$$ 4. **Simplify the exponent:** $$-2 - 6 = -8$$ 5. **Final simplified expression:** $$b^{-8}$$ 6. **Interpretation:** A negative exponent means the reciprocal, so $$b^{-8} = \frac{1}{b^{8}}$$ **Answer:** $$\frac{b^{-2}}{b^{6}} = b^{-8} = \frac{1}{b^{8}}$$