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Zorluk: OrtaOrder of Operations

Determine the final simplified value of the mathematical expression shown below:

−24−3[12−4(3−5)2] -2^4 - 3[12 - 4(3 - 5)^2]

Which of the following represents the correct result?

  1. A
    -112
  2. -4Cevap
  3. C
    28
  4. D
    76

Cevap

The correct simplified value of the expression is -4.
The expression is accurately evaluated by following the standard order of operations. The innermost parentheses are solved to get -2, which is then squared to yield 4. Multiplying this by 4 inside the brackets gives 16, and subtracting this from 12 leaves -4 in the brackets. The leading exponent −24-2^4 is -16. Multiplying the bracket by -3 gives 12, and adding this to -16 yields a final result of -4.

Adım Adım Çözüm

1
Evaluate the expression inside the innermost parentheses: (3−5)(3 - 5).
(3−5)=−2(3 - 5) = -2
According to the order of operations (PEMDAS), parentheses must be resolved first.
2
Apply the exponents to the respective bases: (−2)2(-2)^2 and −24-2^4.
(−2)2=4(-2)^2 = 4 and −24=−16-2^4 = -16
Exponents are evaluated next. Note that −24-2^4 lacks parentheses around the negative sign, meaning it is interpreted as −(24)=−16-(2^4) = -16.
3
Substitute the exponent results back into the bracket and multiply: 4(4)4(4).
The bracket becomes [12−4(4)][12 - 4(4)], which simplifies to [12−16][12 - 16].
Inside the brackets, multiplication must be performed before subtraction.
4
Complete the subtraction inside the brackets: [12−16][12 - 16].
[12−16]=−4[12 - 16] = -4
Finish evaluating the operations grouped by the brackets.
5
Multiply the bracket's result by the coefficient outside: −3(−4)-3(-4).
−3×−4=12-3 \times -4 = 12
Multiplication is performed before the final addition/subtraction.
6
Combine the first term with the multiplication result: −16+12-16 + 12.
−16+12=−4-16 + 12 = -4
Addition and subtraction are the final steps in the order of operations.

Anahtar Kavram

Order of Operations (PEMDAS)
Tahmini Süre:45s
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Konular

Order of Operations

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