Evaluate: $-5+(-3)^2+2$
A. 3
B. 6
C. 1
D. 11
Answer (2)
First, calculate the exponent: ( − 3 ) 2 = 9 .
Then, the expression becomes − 5 + 9 + 2 .
Next, perform the addition from left to right: − 5 + 9 = 4 , so the expression is 4 + 2 .
Finally, add the remaining numbers: 4 + 2 = 6 . The answer is 6 .
Explanation
Understanding the Expression We are asked to evaluate the expression − 5 + ( − 3 ) 2 + 2 . To do this, we need to follow the order of operations (PEMDAS/BODMAS).
Evaluating the Exponent First, we need to evaluate the exponent: ( − 3 ) 2 = ( − 3 ) × ( − 3 ) = 9 . So the expression becomes − 5 + 9 + 2 .
Performing Addition Next, we perform addition from left to right: − 5 + 9 = 4 . So the expression becomes 4 + 2 .
Final Calculation Finally, we add the remaining numbers: 4 + 2 = 6 .
Examples
Understanding how to evaluate expressions like this is fundamental in many areas, such as calculating financial returns, determining the trajectory of objects in physics, or even optimizing processes in engineering. For example, if you invest x dollars and it grows at a rate of r percent per year for t years, the final amount can be calculated using an expression involving exponents and addition. Similarly, in physics, the position of an object under constant acceleration can be described using a quadratic expression.
The evaluation of the expression − 5 + ( − 3 ) 2 + 2 results in 6 . This is found by calculating the exponent first, then performing addition. The correct answer is option B: 6.
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