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What role do exponents play in the order of operations?
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Exponents are handled after parentheses and before multiplication, division, addition, and subtraction in the order of operations.
Evaluate the expression Y^2/(X + Z) - X^2/(Y - X) when Y = 2, X = -3, Z = 4.
Substitute values and simplify to get 11/5 or 2 1/5.
Why is it critical to show your work when evaluating expressions?
Showing work provides a clear, step-by-step trace of operations, helping identify mistakes and verify results.
Describe a common mistake when evaluating expressions with multiplication and division.
A common mistake is failing to perform operations from left to right, such as evaluating 10 ÷ 2 × 3 as 5/3 instead of 15.
Why is it important to follow the order of operations?
Following the order of operations ensures expressions are evaluated correctly, yielding consistent and accurate results.
How do you compute W^2 - 3X when W = √5 and X = -3?
Substitute values and simplify: (√5)^2 = 5 and -3(-3) = 9, so 5 + 9 = 14.
When is the evaluation of absolute values necessary in an expression?
When an expression involves distance or magnitude without regard to direction, absolute values help measure the total numerical value.
In the expression (YZ - X)^2, explain the process of evaluating it with Y = 2, Z = 4, and X = -3.
Substitute values and simplify: (2*4 - (-3)) = 11, so (11)^2 = 121.
How do parentheses affect the evaluation of a complex expression like (YZ - X)^2?
Parentheses specify which operations to perform first, ensuring the correct order and resulting value.
Explain the process of simplifying |3X + Z^2| when X = -3 and Z = 4.
Substitute values and simplify: -9 + 16 gives 7, and the absolute value is |7| = 7.
How does substituting negative values impact the evaluation of an expression?
Negative values require careful attention to signs and may impact operations like subtraction and multiplication.
What is the correct order of operations in algebra?
Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)
What values are assigned to the variables W, X, Y, and Z in evaluating algebraic expressions?
W = √5, X = -3, Y = 2, Z = 4
How do you evaluate the expression 3x^2 + y - 7 when x = -3 and y = 2?
Substitute -3 for x and 2 for y, then calculate: 3(-3)^2 + 2 - 7; this simplifies to 22.
Why is it important to use parentheses when evaluating algebraic expressions?
Parentheses ensure correct interpretation of the expression signs and group terms appropriately for the correct order of operations.
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