1. **State the problem:** Simplify the expression $$\frac{x^6 y^4 z^{-3}}{x^{-2} y^7 z^{-6}}$$ so that all exponents are positive. 2. **Recall the rule for dividing powers with the same base:** $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule to each variable:** $$x^{6 - (-2)} = x^{6 + 2} = x^8$$ $$y^{4 - 7} = y^{-3}$$ $$z^{-3 - (-6)} = z^{-3 + 6} = z^3$$ 4. **Rewrite the expression with these exponents:** $$x^8 y^{-3} z^3$$ 5. **Convert negative exponents to positive by moving the term to the denominator:** $$x^8 z^3 \times y^{-3} = \frac{x^8 z^3}{y^3}$$ **Final simplified expression:** $$\boxed{\frac{x^8 z^3}{y^3}}$$