What is the value of the expression \frac{-2^4 - 6 \times |2 - 2 \times 3|}{2 - (-2)^3} ? — ACT

What is the value of the expression $\frac{-2^4 - 6 \times |2 - 2 \times 3|}{2 - (-2)^3}$ ?

Answer: -4

The value of the expression is

-4

Evaluating the expression step-by-step using order of operations (PEMDAS) yields

-4

. First, simplifying the absolute value

|2 - 2 \times 3|

gives

4

. Next, the exponent

-2^4

evaluates to

-16

, and the exponent

(-2)^3

in the denominator evaluates to

-8

. The numerator simplifies to

-16 - 6(4) = -40

, and the denominator simplifies to

2 - (-8) = 10

. Finally, division gives

-40 \div 10 = -4

Simplify the absolute value expression in the numerator

|2 - 2 \times 3| = |-4| = 4

By the order of operations, multiplication must be performed before subtraction inside the grouping symbols (absolute value).

Evaluate the exponential terms in the numerator and denominator

-2^4 = -16

and

(-2)^3 = -8

In the term

-2^4

, the negative sign is not grouped with the base, so it evaluates to

-(2 \times 2 \times 2 \times 2) = -16

. In

(-2)^3

, the base is negative, evaluating to

(-2) \times (-2) \times (-2) = -8

Calculate the final values of the numerator and the denominator

Numerator =

-40

, Denominator =

10

For the numerator, perform the multiplication before the subtraction:

-16 - (6 \times 4) = -16 - 24 = -40

. For the denominator, subtract the negative number:

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

Divide the numerator by the denominator

-4

The quotient of

-40

and

10

-4

Order of operations (PEMDAS) containing exponents, absolute values, and signed numbers

Estimated Time:1m 15s

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