Verified Answer :

  • Evaluate exponentiation first: \((-6)^2 = 36\).
  • Perform multiplication: \(10 \times 5 = 50\).
  • Combine the results: \(50 - 36 + (-8)\).
  • Perform addition and subtraction from left to right: \(50 - 36 = 14\), then \(14 - 8 = 6\).
  • The final result is \(\boxed{6}\).

Explanation

  1. Evaluating the Numerical Expression

To solve the expression \(10 \times 5 - (-6)^2 + (-8)\), we follow the standard order of operations (often referred to as PEMDAS/BODMAS). This requires us to prioritize parentheses, exponents, multiplication and division, and finally addition and subtraction.

  1. Exponents: First, evaluate the exponentiation \((-6)^2\). Squaring a negative number results in a positive value: \((-6) \times (-6) = 36\).
  2. Multiplication: Next, perform the multiplication \(10 \times 5 = 50\).
  3. Rewrite: Substituting these values back into the original expression, we get: \(50 - 36 + (-8)\).
  4. Addition and Subtraction: Now, proceed from left to right:
  • \(50 - 36 = 14\)
  • \(14 + (-8) = 6\)

Thus, the final value of the expression is \(6\).

Examples

Order of operations is crucial in everyday life, such as when calculating expenses or managing resources. For example, if you are buying 5 items for \$10 each, but you have a discount coupon of \$6 that is squared in a specific reward formula, and then an additional fee of \$8, understanding the order in which these operations are applied ensures you arrive at the correct final cost. This fundamental skill is the foundation for all financial and scientific calculations.

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