1. **State the problem:** Simplify the expression $$(x^{-3} y^{5} z^{-4}) \cdot (x^{6} y^{-7} z^{-2})$$ and verify if the answer $x^{3} y^{-2} z^{-6}$ is correct. 2. **Recall the rule for multiplying powers with the same base:** When multiplying, add the exponents: $$a^{m} \cdot a^{n} = a^{m+n}$$ 3. **Apply the rule to each variable:** - For $x$: $$x^{-3} \cdot x^{6} = x^{-3+6} = x^{3}$$ - For $y$: $$y^{5} \cdot y^{-7} = y^{5 + (-7)} = y^{-2}$$ - For $z$: $$z^{-4} \cdot z^{-2} = z^{-4 + (-2)} = z^{-6}$$ 4. **Combine the results:** $$x^{3} y^{-2} z^{-6}$$ 5. **Conclusion:** The given answer $x^{3} y^{-2} z^{-6}$ is correct.