If x = -2, y = 5, and z = -\frac{1}{2}, what is the value of the algebraic expression \fra… — ACT

If $x = -2$ , $y = 5$ , and $z = -\frac{1}{2}$ , what is the value of the algebraic expression $\frac{x^3 y + z^{-2}}{y - 2x}$ ?

Answer: -4

The value of the expression is -4.

Substituting

x = -2

y = 5

, and

z = -\frac{1}{2}

into the expression yields

x^3 y = (-2)^3(5) = -40

and

z^{-2} = \left(-\frac{1}{2}\right)^{-2} = 4

, making the numerator

-40 + 4 = -36

. Evaluating the denominator gives

y - 2x = 5 - 2(-2) = 9

. Dividing

-36

9

results in

-4

Evaluate the terms in the numerator individually.

x^3 y = (-2)^3(5) = -40

and

z^{-2} = \left(-\frac{1}{2}\right)^{-2} = 4

Negative bases raised to odd powers retain a negative sign, while negative exponents represent the reciprocal raised to a positive power.

Calculate the total numerator value.

-40 + 4 = -36

Summing the two evaluated terms gives the complete numerator.

Evaluate the denominator expression.

y - 2x = 5 - 2(-2) = 5 + 4 = 9

Subtracting a negative quantity is equivalent to adding its positive counterpart.

Divide the numerator by the denominator.

\frac{-36}{9} = -4.

Dividing a negative integer by a positive integer yields a negative quotient.

Evaluating Algebraic Expressions with Negative Integers and Negative Exponents

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