1. **Problem:** Simplify the expression $(-3x^2 y^3 z)(4x^6 y^2 z^{-4})$. 2. **Formula and Rules:** - When multiplying powers with the same base, add the exponents: $a^m \times a^n = a^{m+n}$. - Multiply coefficients normally. - For negative exponents, $a^{-n} = \frac{1}{a^n}$. 3. **Step-by-step simplification:** - Multiply coefficients: $-3 \times 4 = -12$. - For $x$: $x^2 \times x^6 = x^{2+6} = x^8$. - For $y$: $y^3 \times y^2 = y^{3+2} = y^5$. - For $z$: $z^{1} \times z^{-4} = z^{1 + (-4)} = z^{-3}$. 4. **Final simplified expression:** $$-12 x^8 y^5 z^{-3}$$ This matches the given answer, confirming the simplification is correct.