- Evaluate the numerator: \((-4)^2 - 16 = 16 - 16 = 0\).
- Evaluate the denominator: \(6 - 8 = -2\).
- Divide the numerator by the denominator: \(\frac{0}{-2} = 0\).
- The correct choice is A, with the result \(\boxed{0}\).
Explanation
- Analysis of the Expression
The problem requires the evaluation of the expression \(\frac{(-4)^2 - 16}{6 - 8}\). To solve this, we must apply the order of operations, often known by the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). First, we calculate the numerator and the denominator separately before performing the division.
- Evaluating the Numerator
The numerator is given by \((-4)^2 - 16\). First, evaluate the exponent: \((-4)^2 = (-4) \times (-4) = 16\). Now, substitute this back into the numerator expression: \(16 - 16 = 0\). The entire numerator simplifies to 0.
- Evaluating the Denominator
The denominator is given by \(6 - 8\). Performing this subtraction, we get \(6 - 8 = -2\). Since the denominator is \(-2\), which is not zero, the expression is defined.
- Final Calculation and Result
Now we divide the result of the numerator by the result of the denominator: \(\frac{0}{-2} = 0\). Dividing zero by any non-zero number always results in zero. Thus, the expression \(\frac{(-4)^2 - 16}{6 - 8} = 0\). The correct choice is A.
Examples
Understanding the order of operations is crucial in everyday life for tasks such as calculating shared expenses or adjusting recipes. For example, if a bill is \$16 and you have a discount of \$16, the total cost for two people would be \(\frac{16-16}{2} = 0\), meaning everyone eats for free. Similarly, accurate calculation ensures you correctly manage your budget and resources, avoiding errors that could lead to financial or practical misunderstandings.