Verified Answer :

  • Perform the addition inside the parentheses: \(7+3 = 10\).
  • Divide the result by 2: \(10/2 = 5\).
  • Square the result: \(5^2 = 25\).
  • Add the final constant: \(5+25 = 30\).
  • The final answer is \(\boxed{30}\).

Explanation

  1. Analyzing the Expression

The expression given is \(5 + \left(\frac{7+3}{2}\right)^2\). This problem requires following the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). We need to perform the calculations within the parentheses first, followed by exponents, and finally addition.

  1. Evaluating Parentheses

Start by evaluating the sum inside the parentheses: \(7 + 3 = 10\). Now the expression becomes \(5 + \left(\frac{10}{2}\right)^2\). Next, perform the division inside the parentheses: \(10 \div 2 = 5\). The expression simplifies to \(5 + (5)^2\).

  1. Final Calculation and Conclusion

Apply the exponent to the value inside the parentheses: \(5^2 = 5 \times 5 = 25\). Now the expression is \(5 + 25\). Finally, perform the addition: \(5 + 25 = 30\). Thus, the simplified value of the expression is \(30\).

Examples

Order of operations is crucial in everyday financial calculations. For example, if you are calculating the total cost of a project where you have a base fee of \$5 and you are multiplying the result of a divided task cost by itself, you must follow the correct sequence to ensure your budget estimate is accurate. Mastering this ensures that complex real-world calculations are performed correctly.

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