1. **State the problem:** Simplify the expression $$\frac{-8y^7 z^2}{24 y^2}$$. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - Simplify coefficients by dividing their greatest common divisor. 3. **Simplify the coefficients:** $$\frac{-8}{24} = \frac{\cancel{-8}^{\times 1}}{\cancel{24}^{\times 3}} = -\frac{1}{3}$$ 4. **Simplify the variables:** $$\frac{y^7}{y^2} = y^{7-2} = y^5$$ 5. **Combine all parts:** $$-\frac{1}{3} y^5 z^2$$ **Final answer:** $$-\frac{1}{3} y^5 z^2$$