1. **State the problem:** Calculate the value of the expression $$\frac{735 + \sqrt{987,654,321} - 293,847 \times 476}{1,829} + 37^4$$. 2. **Recall formulas and rules:** - Square root: $\sqrt{x}$ is the number which when squared gives $x$. - Exponentiation: $a^b$ means $a$ multiplied by itself $b$ times. - Order of operations: Calculate inside parentheses first, then multiplication and division from left to right, then addition and subtraction. 3. **Calculate each part:** - Calculate $\sqrt{987,654,321}$. - Calculate $293,847 \times 476$. - Calculate $37^4$. 4. **Calculate $\sqrt{987,654,321}$:** $$\sqrt{987,654,321} \approx 31,432.9999$$ (approximate to 4 decimal places) 5. **Calculate $293,847 \times 476$:** $$293,847 \times 476 = 139,491,972$$ 6. **Calculate numerator:** $$735 + 31,432.9999 - 139,491,972 = 735 + 31,432.9999 - 139,491,972$$ $$= 32,167.9999 - 139,491,972 = -139,459,804.0001$$ 7. **Divide numerator by denominator 1,829:** $$\frac{-139,459,804.0001}{1,829}$$ Show cancellation: $$\frac{\cancel{-139,459,804.0001}}{\cancel{1,829}}$$ Calculate division: $$\approx -76,234.9999$$ 8. **Calculate $37^4$:** $$37^4 = 37 \times 37 \times 37 \times 37 = 1,874,161$$ 9. **Add the division result and $37^4$:** $$-76,234.9999 + 1,874,161 = 1,797,926.0001$$ 10. **Final answer:** $$\boxed{1,797,926}$$