Evaluate the expression: $(-2)^2+\left(-4^2\right)+(18-23)$
A) -19
B) 19
C) 3
D) -17
Answer (1)
Calculate ( − 2 ) 2 which equals 4.
Calculate − 4 2 which equals -16.
Calculate ( 18 − 23 ) which equals -5.
Add the results: 4 + ( − 16 ) + ( − 5 ) = − 17 . The final answer is − 17 .
Explanation
Understanding the Expression We are asked to evaluate the expression ( − 2 ) 2 + ( − 4 2 ) + ( 18 − 23 ) . Let's break this down step by step.
Calculating ( − 2 ) 2 First, we calculate ( − 2 ) 2 . This means ( − 2 ) × ( − 2 ) , which equals 4.
Calculating − 4 2 Next, we calculate − 4 2 . Note that this is − ( 4 2 ) , not ( − 4 ) 2 . So, we have − ( 4 × 4 ) = − 16 .
Calculating ( 18 − 23 ) Then, we calculate ( 18 − 23 ) . This equals -5.
Adding the Results Finally, we add the results: 4 + ( − 16 ) + ( − 5 ) = 4 − 16 − 5 = − 12 − 5 = − 17 .
Final Answer Therefore, the value of the expression is -17.
Examples
Understanding how to evaluate expressions with exponents and negative signs is crucial in many areas, such as physics and engineering. For example, when calculating the potential energy of a system or analyzing electrical circuits, you often encounter expressions similar to the one in this problem. Correctly evaluating these expressions ensures accurate results and helps in making informed decisions in practical applications.
