1. **State the problem:** Calculate the value of the expression $$\sqrt[3]{-2} \times (-37) - \{ -2 \times (-3) + 8 \times (-2) - 8 \times 2 \} + 5^2$$. 2. **Recall important rules:** - The cube root of a negative number is negative: $$\sqrt[3]{-a} = -\sqrt[3]{a}$$. - Follow order of operations: parentheses/brackets, exponents, multiplication/division, addition/subtraction. 3. **Calculate each part step-by-step:** - Cube root: $$\sqrt[3]{-2} = -\sqrt[3]{2} \approx -1.26$$ (approximate for calculation). - Multiply: $$-1.26 \times (-37) = 46.62$$. 4. **Evaluate the bracketed expression:** - $$-2 \times (-3) = 6$$ - $$8 \times (-2) = -16$$ - $$-8 \times 2 = -16$$ - Sum inside brackets: $$6 - 16 - 16 = 6 - 32 = -26$$ 5. **Calculate the exponent:** - $$5^2 = 25$$ 6. **Combine all parts:** - Expression becomes $$46.62 - (-26) + 25 = 46.62 + 26 + 25 = 97.62$$ 7. **Final answer:** $$\boxed{97.62}$$ (rounded to two decimal places).