1. **State the problem:** Simplify the expression $$(-3xy^{-5} z^8) \times (2x^{-3} y^2)$$. 2. **Write the expression:** $$-3xy^{-5} z^8 \times 2x^{-3} y^2$$. 3. **Multiply the coefficients:** $$-3 \times 2 = -6$$. 4. **Apply the product rule for exponents:** When multiplying like bases, add the exponents. For $x$: $$x^{1} \times x^{-3} = x^{1 + (-3)} = x^{-2}$$. For $y$: $$y^{-5} \times y^{2} = y^{-5 + 2} = y^{-3}$$. For $z$: $$z^{8}$$ (no $z$ term in second factor, so exponent remains 8). 5. **Combine all parts:** $$-6 x^{-2} y^{-3} z^{8}$$. 6. **Rewrite with positive exponents:** $$-6 \frac{z^{8}}{x^{2} y^{3}}$$. **Final answer:** $$-6 \frac{z^{8}}{x^{2} y^{3}}$$.