If x = -3, y = -\frac{1}{2}, and z = 8, what is the value of the algebraic expression \fra… — ACT

If $x = -3$ , $y = -\frac{1}{2}$ , and $z = 8$ , what is the value of the algebraic expression $\frac{x^2 y^{-1} + z^{2/3}}{2xy - 1}$ ?

Answer: -7

The value of the expression is -7.

Substituting the given values into the expression requires careful application of exponent rules and order of operations. First,

(-3)^2 = 9

and

(-\frac{1}{2})^{-1} = -2

, so

x^2 y^{-1} = 9 \times (-2) = -18

. Second,

8^{2/3} = (\sqrt[3]{8})^2 = 2^2 = 4

. This makes the numerator

-18 + 4 = -14

. The denominator evaluates to

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

. Dividing

-14

2

gives the correct answer of

-7

Substitute

x = -3

and

y = -\frac{1}{2}

into

x^2 y^{-1}

(-3)^2 \cdot (-2) = -18

Squaring

-3

yields

9

, and taking the reciprocal of

-\frac{1}{2}

yields

-2

Substitute

z = 8

into

z^{2/3}

8^{2/3} = 4

Taking the cube root of

8

gives

2

, and squaring

2

gives

4

Evaluate the numerator

-18 + 4 = -14

Adding the evaluated terms together.

Substitute values into the denominator

2xy - 1

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

Multiplying

2

-3

, and

-\frac{1}{2}

produces

3

, then subtracting

1

yields

2

Divide the numerator by the denominator

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

Simplifying the rational expression yields the final numeric answer.

Evaluating algebraic expressions with negative bases, rational exponents, and negative exponents

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