Determine the exact value of the expression below by applying the correct sequence of math… — Armed Services Vocational Aptitude Battery (ASVAB)

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

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

Which of the following represents the correct numerical result?

Following the proper order of operations, we first simplify the parentheses to get -2. Next, we apply the exponent:

(-2)^3

equals -8. Then we perform multiplication and division:

-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 - 4

, which evaluates to 32.

Evaluate the expression inside the parentheses:

(3 - 5)

-2

According to the order of operations, operations inside parentheses must be resolved first.

Apply the exponent to the result of the parentheses:

(-2)^3

-8

Exponents must be evaluated before multiplication or division.

Perform the multiplication:

-2 \times (-8)

Multiplication is performed left-to-right before any addition or subtraction. Note that multiplying two negative numbers yields a positive result.

Perform the division:

\frac{-16}{4}

-4

Division is also resolved before addition and subtraction. A negative divided by a positive yields a negative result.

Complete the final addition and subtraction left-to-right:

20 + 16 - 4

Once all higher-order operations are complete, add and subtract from left to right.

Order of Operations with Signed Numbers and Exponents

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