Textbook Question
Find each product. (4x2-5y)(4x2+5y)
Ch. R - Review of Basic Concepts
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 1, Problem 45
Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. 4x-2
Verified step by step guidance1
Identify the expression given: \(4x^{-2}\). The negative exponent indicates the reciprocal of the base raised to the positive exponent.
Rewrite the expression by applying the rule \(a^{-n} = \frac{1}{a^n}\), so \(x^{-2}\) becomes \(\frac{1}{x^2}\).
Substitute this back into the expression to get \(4 \times \frac{1}{x^2}\).
Simplify the expression by writing it as a single fraction: \(\frac{4}{x^2}\).
Since the problem states to evaluate if possible and variables represent nonzero real numbers, this is the simplified form without negative exponents.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, x⁻² equals 1/x². Understanding this allows rewriting expressions without negative exponents by moving factors between numerator and denominator.
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Zero and Negative Rules
Simplifying Algebraic Expressions
Simplifying involves rewriting expressions in a more straightforward form by applying exponent rules and combining like terms. This process helps in expressing terms without negative exponents and prepares the expression for evaluation.
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Evaluating Expressions with Variables
Evaluating an expression means substituting given values for variables and calculating the result. Since variables are nonzero, division by zero is avoided, ensuring the expression with negative exponents rewritten as fractions can be safely evaluated.
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Related Practice
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Find each sum or difference. 9/10 - (-4/3)
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Factor each trinomial, if possible. See Examples 3 and 4.
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Multiply or divide as indicated. Write answers in lowest terms as needed.
Textbook Question
Determine whether each statement is true or false. {3, 0, 9, 6, 2} = {2, 9, 0, 3, 6}
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Factor each trinomial, if possible. See Examples 3 and 4. 5a2-7ab-6b2