Examkin

Soru

Zorluk: Çok zorEvaluating Algebraic Expressions

Evaluate the algebraic expression below given that x=−4x = -4, y=−2y = -2, and z=−3z = -3:

x3−y2(x−z)∣x∣−z2 \frac{x^3 - y^2(x - z)}{|x| - z^2}

Calculate the intermediate values and the final result to complete the statements.

Cevap:The value of the numerator is 【-60】.
The value of the denominator is 【-5】.
The final evaluated result of the expression is 【12】.

Cevap

The numerator evaluates to -60, the denominator evaluates to -5, and the final evaluated result of the expression is 12.
By strictly adhering to the order of operations and properly handling negative substitutions, the numerator simplifies to -60 and the denominator simplifies to -5. Dividing these yields a final positive integer result of 12.

Adım Adım Çözüm

1
Substitute the given values for xx, yy, and zz into the expression.
(−4)3−(−2)2(−4−(−3))∣−4∣−(−3)2 \frac{(-4)^3 - (-2)^2(-4 - (-3))}{|-4| - (-3)^2}
Direct substitution is the required first step before performing any operations.
2
Evaluate the exponents in the numerator and denominator.
Numerator exponents: (−4)3=−64(-4)^3 = -64 and (−2)2=4(-2)^2 = 4. Denominator exponent: (−3)2=9(-3)^2 = 9.
Following the order of operations, exponents must be evaluated before multiplication and subtraction.
3
Evaluate the expression inside the parentheses in the numerator and the absolute value in the denominator.
Numerator parentheses: (−4−(−3))=(−4+3)=−1(-4 - (-3)) = (-4 + 3) = -1. Denominator absolute value: ∣−4∣=4|-4| = 4.
Operations inside grouping symbols and absolute value operations take precedence.
4
Perform the remaining multiplication in the numerator, then subtract to find the final numerator value.
−64−(4)(−1)=−64−(−4)=−64+4=−60-64 - (4)(-1) = -64 - (-4) = -64 + 4 = -60. (Value for blank 1)
Multiplication is performed before addition or subtraction according to the order of operations.
5
Perform the subtraction in the denominator.
4−9=−54 - 9 = -5. (Value for blank 2)
This fully simplifies the expression in the denominator.
6
Divide the fully simplified numerator by the simplified denominator.
−60−5=12 \frac{-60}{-5} = 12 . (Value for blank 3)
The fraction bar represents division, which is the final operation applied to the evaluated top and bottom terms.

Anahtar Kavram

Evaluating Complex Algebraic Expressions
Bu soruyu puanla

Konular

Evaluating Algebraic Expressions

Bu konudan daha fazla soru