1. **State the problem:** Simplify the expression $$\sqrt[3]{-2x(-37)} - \left[-2(-3) + 8x(-2) - 8x2\right] + 5^2$$ where the $x$ symbols are variables, not multiplication signs. 2. **Rewrite the expression clearly:** $$\sqrt[3]{-2x(-37)} - \left[-2(-3) + 8x(-2) - 8x2\right] + 5^2$$ 3. **Simplify inside the cube root:** Inside the cube root, multiply $-2x$ by $-37)$: $$-2x \times (-37) = 74x$$ So the cube root becomes: $$\sqrt[3]{74x}$$ 4. **Simplify the bracketed expression:** Calculate each term inside the brackets: - $-2(-3) = 6$ - $8x(-2) = -16x$ - $-8x2 = -16x$ So the bracket is: $$6 - 16x - 16x = 6 - 32x$$ 5. **Rewrite the full expression:** $$\sqrt[3]{74x} - [6 - 32x] + 5^2$$ 6. **Remove the brackets (distribute the minus sign):** $$\sqrt[3]{74x} - 6 + 32x + 25$$ 7. **Simplify constants:** $$-6 + 25 = 19$$ 8. **Final simplified expression:** $$\sqrt[3]{74x} + 32x + 19$$ **Answer:** $$\boxed{\sqrt[3]{74x} + 32x + 19}$$