What is the value of the expression below? \frac{-2^4 - |-12 + (-2)^3|}{(-1)^5 \times 3^2 … — ACT

What is the value of the expression below?

\frac{-2^4 - |-12 + (-2)^3|}{(-1)^5 \times 3^2 - (-2)^3} \div \left( \frac{1}{3} - 1 \right)

-54

Evaluating the numerator gives

-36

, and the denominator simplifies to

-1

, resulting in a fraction of

36

. Dividing

36

(1/3 - 1) = -2/3

is performed by multiplying

36

by the reciprocal

-3/2

, which yields the final result of

-54

Evaluate the numerator of the first fraction.

Numerator =

-36

First, evaluate the exponent inside the absolute value:

(-2)^3 = -8

. Next, evaluate the expression inside the absolute value:

-12 + (-8) = -20

. Taking the absolute value gives

|-20| = 20

. Separately, evaluate the exponent

-2^4 = -(2^4) = -16

because exponentiation has priority over negation. Finally, subtract the absolute value term from this to get

-16 - 20 = -36

Evaluate the denominator of the first fraction.

Denominator =

-1

Evaluate the exponents first:

(-1)^5 = -1

3^2 = 9

, and

(-2)^3 = -8

. Then, perform the multiplication:

-1 \times 9 = -9

. Finally, perform the subtraction:

-9 - (-8) = -9 + 8 = -1

Simplify the first fraction.

Fraction =

36

Divide the numerator by the denominator:

\frac{-36}{-1} = 36

Evaluate the expression inside the divisor parentheses.

Divisor =

-\frac{2}{3}

Perform the fraction subtraction:

\frac{1}{3} - 1 = \frac{1}{3} - \frac{3}{3} = -\frac{2}{3}

Divide the simplified fraction by the divisor.

Final Value =

-54

To divide by a fraction, multiply by its reciprocal:

36 \div \left(-\frac{2}{3}\right) = 36 \times \left(-\frac{3}{2}\right) = 18 \times (-3) = -54

Order of Operations (PEMDAS) and Number Properties

Question