If r = -3, s = 2, and t = -\frac{1}{2}, what is the value of the algebraic expression \fra… — ACT

If $r = -3$ , $s = 2$ , and $t = -\frac{1}{2}$ , what is the value of the algebraic expression $\frac{r^2 s - t^{-2}}{r + s t}$ ?

-\frac{7}{2}

Substituting

r = -3

s = 2

, and

t = -\frac{1}{2}

into the numerator yields

(-3)^2(2) - \left(-\frac{1}{2}\right)^{-2} = (9)(2) - 4 = 18 - 4 = 14

. Substituting into the denominator yields

-3 + 2\left(-\frac{1}{2}\right) = -3 - 1 = -4

. Dividing numerator by denominator gives

\frac{14}{-4} = -\frac{7}{2}

Substitute the given variable values into the numerator expression

r^2 s - t^{-2}

Numerator =

(-3)^2 (2) - \left(-\frac{1}{2}\right)^{-2}

Ensure negative values are enclosed in parentheses during substitution.

Evaluate the terms in the numerator following order of operations and exponent rules.

(-3)^2 = 9

, so

9 \cdot 2 = 18

. Also

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

. Thus, Numerator =

18 - 4 = 14

A negative base squared yields a positive value, and a negative exponent takes the reciprocal of the base.

Substitute values into the denominator expression

r + s t

and simplify.

Denominator =

-3 + (2)\left(-\frac{1}{2}\right) = -3 + (-1) = -4

Multiply

s

and

t

first before adding to

r

according to PEMDAS.

Divide the evaluated numerator by the evaluated denominator.

\frac{14}{-4} = -\frac{7}{2}

Simplify the fraction by dividing both numerator and denominator by 2.

Evaluating Algebraic Expressions with Negative Bases and Negative Exponents

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