Verified Answer :

  • Evaluate the exponent \(4^2 = 16\).
  • Multiply the first two numbers: \(3 \times 10 = 30\).
  • Perform addition: \(30 + 8 = 38\).
  • Subtract the result of the exponent: \(38 - 16 = 22\).
  • The final result is \(\boxed{22}\).

Explanation

  1. Understanding the Problem and Rules of Operation

To solve the expression \(3 \times 10 + 8 - 4^2\), we must follow the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This standard ensures that mathematical expressions are evaluated consistently. The expression involves an exponent, multiplication, addition, and subtraction.

  1. Evaluating the Exponent

The first step in the order of operations is to evaluate any exponents. We have \(4^2\), which means \(4 \times 4\). Thus, \(4^2 = 16\). Replacing this in our expression gives:
\[3 \times 10 + 8 - 16\]

  1. Performing Multiplication

Next, we perform multiplication. We have the term \(3 \times 10\). Evaluating this, we get \(30\). Now, substitute this value back into the expression:
\[30 + 8 - 16\]

  1. Performing Addition and Subtraction

Finally, we perform addition and subtraction from left to right. First, add: \(30 + 8 = 38\). Then, subtract: \(38 - 16 = 22\). The final value of the expression is \(\boxed{22}\).

Examples

Understanding the order of operations is crucial in everyday financial calculations, such as determining the final cost of an order. For instance, if you buy 3 packs of pens at \(\$10\) each, add an \(\$8\) processing fee, and then subtract a \(\$16\) discount, the expression \(3 \times 10 + 8 - 16\) correctly calculates your final balance of \(\$22\). Applying these rules ensures that bills, receipts, and budgets are calculated accurately and fairly.

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