1. **State the problem:** Calculate the value of $$73^5 + \sqrt{987654321} - \frac{293847 \times 476}{1829} + 37^4$$. 2. **Recall formulas and rules:** - Exponentiation: $$a^b$$ means multiplying $$a$$ by itself $$b$$ times. - Square root: $$\sqrt{x}$$ is the number which when squared gives $$x$$. - Order of operations: Calculate powers and roots first, then multiplication and division, and finally addition and subtraction. 3. **Calculate powers:** - $$73^5 = 73 \times 73 \times 73 \times 73 \times 73 = 201,511,533,073$$ - $$37^4 = 37 \times 37 \times 37 \times 37 = 1,874,161$$ 4. **Calculate square root:** - $$\sqrt{987654321} \approx 31,432.99$$ (rounded to two decimals) 5. **Calculate multiplication and division:** - Multiply: $$293,847 \times 476 = 139,857,372$$ - Divide: $$\frac{139,857,372}{1829} \approx 76,441.68$$ 6. **Combine all parts:** $$201,511,533,073 + 31,432.99 - 76,441.68 + 1,874,161$$ 7. **Simplify step-by-step:** - $$201,511,533,073 + 31,432.99 = 201,511,564,505.99$$ - $$201,511,564,505.99 - 76,441.68 = 201,511,488,064.31$$ - $$201,511,488,064.31 + 1,874,161 = 201,513,362,225.31$$ **Final answer:** $$201,513,362,225.31$$