What is the integer value of the expression -4^2 + | -15 \div 3 \times 2 | - (-3)^3? — ACT

What is the integer value of the expression $-4^2 + | -15 \div 3 \times 2 | - (-3)^3$ ?

Answer: 21

The correct answer is 21.

The correct answer is obtained by strictly following the order of operations (PEMDAS): first evaluating exponents (

-4^2 = -16

and

(-3)^3 = -27

), then performing the operations inside the absolute value from left to right (

-15 \div 3 = -5

followed by

-5 \times 2 = -10

, which simplifies to

|-10| = 10

), and finally executing addition and subtraction from left to right (

-16 + 10 - (-27) = 21

Evaluate the exponent

-4^2

-16

According to the order of operations, the exponent is applied to the base 4 first, and then the negation is applied, yielding

-(4^2) = -16

Evaluate the absolute value expression

|-15 \div 3 \times 2|

10

Multiplication and division have the same precedence and must be performed from left to right: first

-15 \div 3 = -5

, then

-5 \times 2 = -10

. Taking the absolute value of

-10

yields

10

Evaluate the exponent

(-3)^3

-27

Since the negative sign is inside the parentheses, the base is

-3

, so

(-3)^3 = (-3) \times (-3) \times (-3) = -27

Combine the values and simplify

21

Substitute the evaluated parts into the original expression:

-16 + 10 - (-27)

. Simplify by performing addition and subtraction from left to right:

-16 + 10 = -6

, and

-6 - (-27) = -6 + 27 = 21

Order of operations (PEMDAS) and absolute value properties

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