1. **State the problem:** Simplify the expression $$\frac{a^{-1} b^{-2} c^{-6}}{4}$$ and express it as a single fraction with positive exponents. 2. **Recall the rule for negative exponents:** For any variable $x$ and integer $n$, $$x^{-n} = \frac{1}{x^n}$$. This means negative exponents indicate the reciprocal. 3. **Apply the rule to each term:** $$a^{-1} = \frac{1}{a^1} = \frac{1}{a}$$ $$b^{-2} = \frac{1}{b^2}$$ $$c^{-6} = \frac{1}{c^6}$$ 4. **Rewrite the original expression:** $$\frac{a^{-1} b^{-2} c^{-6}}{4} = \frac{\frac{1}{a} \cdot \frac{1}{b^2} \cdot \frac{1}{c^6}}{4} = \frac{1}{4} \cdot \frac{1}{a b^2 c^6} = \frac{1}{4 a b^2 c^6}$$ 5. **Final simplified expression:** $$\boxed{\frac{1}{4 a b^2 c^6}}$$ This means the exponents to fill in the boxes are $1$ for $a$, $2$ for $b$, and $6$ for $c$ in the denominator.