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Difficulty: MediumOrder of Operations

Determine the exact value of the expression below by applying the correct sequence of mathematical operations:

20−2×(3−5)3+−164 20 - 2 \times (3 - 5)^3 + \frac{-16}{4}

Which of the following represents the correct numerical result?

  1. A
    0
  2. B
    -148
  3. 32Answer
  4. D
    80

Answer

32
Following the proper order of operations, we first simplify the parentheses to get -2. Next, we apply the exponent: (−2)3(-2)^3 equals -8. Then we perform multiplication and division: −2×−8-2 \times -8 gives a positive 16, and dividing -16 by 4 gives -4. Finally, substituting these values back into the expression leaves 20+16−420 + 16 - 4, which evaluates to 32.

Step-by-Step Solution

1
Evaluate the expression inside the parentheses: (3−5)(3 - 5)
-2
According to the order of operations, operations inside parentheses must be resolved first.
2
Apply the exponent to the result of the parentheses: (−2)3(-2)^3
-8
Exponents must be evaluated before multiplication or division.
3
Perform the multiplication: −2×(−8)-2 \times (-8)
16
Multiplication is performed left-to-right before any addition or subtraction. Note that multiplying two negative numbers yields a positive result.
4
Perform the division: −164\frac{-16}{4}
-4
Division is also resolved before addition and subtraction. A negative divided by a positive yields a negative result.
5
Complete the final addition and subtraction left-to-right: 20+16−420 + 16 - 4
32
Once all higher-order operations are complete, add and subtract from left to right.

Key Concept

Order of Operations with Signed Numbers and Exponents
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Topics

Order of Operations

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