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Question

Difficulty: HardOrder of Operations and Number Properties

What is the value of the expression below?

−[(−3)2−∣4−2×5∣]×23−18÷3×(−2)−3+1 -[(-3)^2 - |4 - 2 \times 5|] \times 2^3 - \frac{18 \div 3 \times (-2)}{-3 + 1}

Answer: -30

Answer

The value of the expression is −30-30.
Applying the correct order of operations (PEMDAS) ensures the expression is evaluated systematically. Evaluating the first term gives −[(−3)2−∣4−2×5∣]×23=−[9−∣−6∣]×8=−[9−6]×8=−3×8=−24-[(-3)^2 - |4 - 2 \times 5|] \times 2^3 = -[9 - |-6|] \times 8 = -[9 - 6] \times 8 = -3 \times 8 = -24. Evaluating the fraction term gives 18÷3×(−2)−3+1=6×(−2)−2=−12−2=6\frac{18 \div 3 \times (-2)}{-3 + 1} = \frac{6 \times (-2)}{-2} = \frac{-12}{-2} = 6. Subtracting the fraction value from the first term results in −24−6=−30-24 - 6 = -30.

Step-by-Step Solution

1
Simplify the grouping symbols: the bracket and absolute value term.
−3-3
First, evaluate the exponent (−3)2=9(-3)^2 = 9. Inside the absolute value, multiplication takes precedence over subtraction: 4−2×5=4−10=−64 - 2 \times 5 = 4 - 10 = -6. The absolute value is ∣−6∣=6|-6| = 6. Subtracting this from 99 inside the brackets gives 33. Finally, apply the negative sign in front of the brackets to get −3-3.
2
Evaluate the exponent 232^3 and perform the multiplication.
−24-24
Exponents are evaluated before multiplication. Since 23=82^3 = 8, the multiplication becomes −3×8=−24-3 \times 8 = -24.
3
Evaluate the fraction term.
66
In the numerator, multiplication and division are performed from left to right: 18÷3=618 \div 3 = 6, then 6×(−2)=−126 \times (-2) = -12. The denominator evaluates to −3+1=−2-3 + 1 = -2. Dividing the numerator by the denominator gives −12−2=6\frac{-12}{-2} = 6.
4
Perform the final subtraction.
−30-30
Subtract the evaluated fraction value from the first term: −24−6=−30-24 - 6 = -30.

Key Concept

Order of operations (PEMDAS), absolute value, and exponent rules with signed numbers.

Alternative Method

Evaluate each major term separately, paying close attention to grouping symbols, negative signs, and the left-to-right order for multiplication and division.
Estimated Time:2m 30s
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Topics

Order of Operations and Number Properties

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