Given the values x = \frac{1}{2}, y = -4, and z = -2, determine the value of the expressio… — Armed Services Vocational Aptitude Battery (ASVAB)

Given the values $x = \frac{1}{2}$ , $y = -4$ , and $z = -2$ , determine the value of the expression $4x^2y - yz^3$ .

Answer: -36

Answer

-36

The correct answer is derived by substituting the variables accurately, applying the exponents (especially noting that a negative base to an odd power remains negative), and strictly following the order of operations to multiply and then subtract.

Step-by-Step Solution

Substitute

x = \frac{1}{2}

y = -4

, and

z = -2

into the expression.

4(\frac{1}{2})^2(-4) - (-4)(-2)^3

Variable substitution must be done exactly as given to prepare for evaluation.

Evaluate the terms with exponents.

(\frac{1}{2})^2 = \frac{1}{4}

and

(-2)^3 = -8

. The expression becomes

4(\frac{1}{4})(-4) - (-4)(-8)

According to the order of operations (PEMDAS), exponents must be resolved before multiplication.

Perform the multiplication operations from left to right.

4(\frac{1}{4})(-4) = 1(-4) = -4

and

(-4)(-8) = 32

. The expression is now

-4 - 32

Multiplication is the next step in the order of operations. Note that multiplying two negative numbers results in a positive product.

Perform the final subtraction.

-4 - 32 = -36

Subtracting a positive number from a negative number moves further left on the number line.

Key Concept

Evaluating algebraic expressions using rational numbers, negative bases, and the correct order of operations.

Estimated Time:1m 0s

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