What is the value of the expression \frac{3 \times 4^2 - 2 \times (5 - 8)^2}{2 - (-2)^3}? — ACT

What is the value of the expression $\frac{3 \times 4^2 - 2 \times (5 - 8)^2}{2 - (-2)^3}$ ?

Answer: 3

The value of the expression is 3.

Following the standard order of operations (PEMDAS), we first calculate the expression inside the parentheses:

5 - 8 = -3

. We then evaluate the exponents:

4^2 = 16

(-3)^2 = 9

, and

(-2)^3 = -8

. Substituting these back into the expression, the numerator becomes

3(16) - 2(9) = 48 - 18 = 30

, and the denominator becomes

2 - (-8) = 2 + 8 = 10

. Dividing the numerator by the denominator gives

\frac{30}{10} = 3

Simplify the grouping inside the parentheses

5 - 8 = -3

According to the order of operations, terms inside grouping symbols must be evaluated first.

Evaluate the exponential terms

4^2 = 16

(-3)^2 = 9

, and

(-2)^3 = -8

Exponents are evaluated next after parentheses.

Perform multiplication in the numerator

3 \times 16 = 48

and

2 \times 9 = 18

Multiplication has priority over subtraction.

Simplify the numerator and the denominator by performing subtraction and addition

Numerator:

48 - 18 = 30

; Denominator:

2 - (-8) = 10

Addition and subtraction are performed next from left to right.

Divide the simplified numerator by the simplified denominator

\frac{30}{10} = 3

Perform the final division to find the value of the fraction.

Order of Operations

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