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Difficulty: MediumOrder of Operations and Number Properties

What is the value of the mathematical expression below?

−18÷3×2−(6−8)3-18 \div 3 \times 2 - (6 - 8)^3
  1. A
    -60
  2. B
    -20
  3. C
    -6
  4. -4Answer
  5. E
    5

Answer

-4
Evaluating the expression according to the order of operations (PEMDAS) yields the correct value. First, simplify the expression within the parentheses to get 6−8=−26 - 8 = -2. Second, evaluate the exponent to get (−2)3=−8(-2)^3 = -8. Next, perform multiplication and division from left to right: first divide −18-18 by 33 to get −6-6, then multiply by 22 to get −12-12. Finally, perform the subtraction: −12−(−8)=−12+8=−4-12 - (-8) = -12 + 8 = -4.

Step-by-Step Solution

1
Evaluate the expression inside the parentheses.
6 - 8 = -2
According to the order of operations (PEMDAS), operations inside parentheses must be evaluated first.
2
Evaluate the exponent.
(-2)^3 = -8
Exponents are evaluated next. A negative number raised to an odd power yields a negative result.
3
Perform the division.
−18÷3=−6-18 \div 3 = -6
Multiplication and division have equal priority and must be performed from left to right.
4
Perform the multiplication.
−6×2=−12-6 \times 2 = -12
Continuing from left to right, perform the multiplication next.
5
Perform the subtraction.
-12 - (-8) = -12 + 8 = -4
Finally, perform the subtraction. Subtracting a negative number is equivalent to adding its positive counterpart.

Key Concept

Order of Operations (PEMDAS) with negative numbers and exponents
Estimated Time:1m 0s
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Topics

Order of Operations and Number Properties

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