Simplify the expression completely.
$(-7)^2-132 \div(17-5)$
Answer (2)
Evaluate the exponent: ( − 7 ) 2 = 49 .
Evaluate the parentheses: ( 17 − 5 ) = 12 .
Perform the division: 132 d i v 12 = 11 .
Perform the subtraction: 49 − 11 = 38 . The simplified expression is 38 .
Explanation
Understanding the Expression We are asked to simplify the expression ( − 7 ) 2 − 132 d i v ( 17 − 5 ) . To do this, we will follow the order of operations (PEMDAS/BODMAS).
Evaluating the Exponent First, we evaluate the exponent: ( − 7 ) 2 = ( − 7 ) × ( − 7 ) = 49 .
Evaluating the Parentheses Next, we evaluate the expression inside the parentheses: ( 17 − 5 ) = 12 .
Performing the Division Now, we perform the division: 132 d i v 12 = 11 .
Performing the Subtraction Finally, we perform the subtraction: 49 − 11 = 38 .
Final Answer Therefore, the simplified expression is 38 .
Examples
Understanding order of operations is crucial in many real-life scenarios, such as calculating expenses, determining the outcome of a scientific experiment, or even following a recipe. For example, if you are calculating the total cost of a project that involves both fixed costs and variable costs depending on the number of units produced, you need to follow the correct order of operations to arrive at the correct total cost. Similarly, in programming, the order in which operations are performed can significantly affect the outcome of a calculation, making it essential to understand and apply the correct order of operations.
The simplified expression is 38, derived by evaluating the exponent, solving the parentheses, performing the division, and finally subtracting the results. Following the order of operations ensures that we arrive at the correct result. Each step contributes to simplifying the expression systematically.
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