1. **State the problem:** Simplify the expression $$\frac{6b^6 a^{-3}}{36a^{-2} b^{-7}}$$ and write the answer using only positive exponents. 2. **Recall the quotient rule for exponents:** When dividing like bases, subtract the exponents: $$\frac{x^m}{x^n} = x^{m-n}$$. 3. **Simplify the coefficients:** $$\frac{6}{36} = \frac{\cancel{6}}{\cancel{36}} = \frac{1}{6}$$. 4. **Simplify the variable $a$ terms:** $$a^{-3} \div a^{-2} = a^{-3 - (-2)} = a^{-3 + 2} = a^{-1}$$. 5. **Simplify the variable $b$ terms:** $$b^{6} \div b^{-7} = b^{6 - (-7)} = b^{6 + 7} = b^{13}$$. 6. **Combine all parts:** $$\frac{1}{6} \times a^{-1} \times b^{13} = \frac{b^{13}}{6a}$$. 7. **Final answer with only positive exponents:** $$\boxed{\frac{b^{13}}{6a}}$$.