1. **State the problem:** Evaluate the expression $$\sqrt[3]{-8} \times \left(12 - \left(5^2 + \sqrt{9}\right)\right) \div 8$$. 2. **Recall important rules:** - Cube root of a number $a$ is a number $b$ such that $b^3 = a$. - Order of operations: parentheses first, then exponents and roots, then multiplication and division from left to right. 3. **Calculate inside the innermost parentheses:** $$5^2 = 25$$ $$\sqrt{9} = 3$$ So, $$5^2 + \sqrt{9} = 25 + 3 = 28$$ 4. **Substitute back and simplify inside the parentheses:** $$12 - 28 = -16$$ 5. **Calculate the cube root:** $$\sqrt[3]{-8} = -2$$ because $(-2)^3 = -8$ 6. **Rewrite the expression:** $$-2 \times (-16) \div 8$$ 7. **Multiply:** $$-2 \times (-16) = 32$$ 8. **Divide:** $$32 \div 8 = 4$$ **Final answer:** $$4$$