Evaluate the following algebraic expression given x = -3, y = 2, and z = -5: x^2 - \frac{y… — Armed Services Vocational Aptitude Battery (ASVAB)

Evaluate the following algebraic expression given $x = -3$ , $y = 2$ , and $z = -5$ :

x^2 - \frac{y^3 z}{|x + z|}

Fill in the blanks with the correct numerical values.

Answer:The evaluated value of the fraction term alone (i.e.,

\frac{y^3 z}{|x + z|}

) is 【-5】, which makes the final value of the entire expression equal to 【14】.

The fraction term evaluates to -5, and the final expression evaluates to 14.

By following the order of operations (PEMDAS), we first substitute the values and handle operations inside grouping symbols like absolute value (

|-3 + -5| = 8

). Next, exponents are calculated (

(-3)^2 = 9

and

2^3 = 8

), followed by multiplication and division to simplify the fraction to

-5

. Finally, subtracting this negative value gives

9 - (-5) = 14

Substitute the given values into the expression.

(-3)^2 - \frac{2^3(-5)}{|-3 + (-5)|}

Direct variable substitution according to the given values is the first step in evaluating any algebraic expression.

Evaluate the numerator of the fraction.

2^3(-5) = 8(-5) = -40

According to the order of operations, exponents must be evaluated before multiplication.

Evaluate the denominator of the fraction.

|-3 + (-5)| = |-8| = 8

Grouping symbols, such as absolute value bars, must be evaluated from the inside out.

Divide the numerator by the denominator to find the fraction term's value.

\frac{-40}{8} = -5

Division within the fraction is performed before interacting with the rest of the expression.

Evaluate the squared term and subtract the fraction's value.

9 - (-5) = 9 + 5 = 14

Exponents are evaluated first, and subtracting a negative number is mathematically equivalent to adding a positive number.

Evaluating multi-step algebraic expressions involving negative bases, absolute values, and fractions.

Estimated Time:1m 0s

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