What is the value of the expression -3 \times (4 - 7)^2 + \frac{24}{2^3 - 4}? — ACT

What is the value of the expression $-3 \times (4 - 7)^2 + \frac{24}{2^3 - 4}$ ?

The correct answer is

-21

Following the order of operations, we first compute the term inside the parentheses:

4 - 7 = -3

. Next, we evaluate the exponents:

(-3)^2 = 9

and

2^3 = 8

. This simplifies the expression to

-3 \times 9 + \frac{24}{8 - 4}

. Simplifying the denominator gives

8 - 4 = 4

. We then perform the multiplication and division:

-3 \times 9 = -27

and

\frac{24}{4} = 6

. Adding these results together yields

-27 + 6 = -21

Evaluate the subtraction inside the parentheses.

4 - 7 = -3

According to the order of operations, grouping symbols such as parentheses must be evaluated first.

Evaluate the exponential terms in the expression.

(-3)^2 = 9

and

2^3 = 8

Exponents must be evaluated after parentheses and before multiplication, division, addition, or subtraction.

Simplify the denominator of the fraction.

8 - 4 = 4

The denominator must be fully simplified before dividing the numerator by it.

Perform multiplication and division from left to right.

-3 \times 9 = -27

and

\frac{24}{4} = 6

Multiplication and division have higher priority than addition and subtraction.

Perform the final addition.

-27 + 6 = -21

Addition and subtraction are performed last.

Order of Operations (PEMDAS)

Question