Textbook Question
Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places.
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 89
In Exercises 83–90, perform the indicated operation or operations. (2x−7)5/(2x−7)3
Verified step by step guidance1
Identify the given expression: \((2x - 7)^5 / (2x - 7)^3\). This is a division of exponential expressions with the same base \((2x - 7)\).
Recall the property of exponents: \(\frac{a^m}{a^n} = a^{m-n}\), where \(a\) is the base, and \(m\) and \(n\) are the exponents. Apply this property to simplify the expression.
Subtract the exponents: \(5 - 3\). This gives the new exponent for the base \((2x - 7)\).
Rewrite the simplified expression as \((2x - 7)^2\).
The final simplified expression is \((2x - 7)^2\). You can leave it in this form or expand it further if needed.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponents and Power Rules
Understanding exponents is crucial in algebra, particularly the power rules which state that when dividing like bases, you subtract the exponents. For example, a^m / a^n = a^(m-n). This rule simplifies expressions involving powers and is essential for solving the given problem.
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Power Rules
Simplifying Algebraic Expressions
Simplifying algebraic expressions involves reducing them to their simplest form. This process often includes combining like terms and applying exponent rules. In the context of the given question, simplifying (2x−7)^5/(2x−7)^3 requires applying the exponent subtraction rule to achieve a more manageable expression.
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Polynomial Functions
Polynomial functions are expressions that involve variables raised to whole number exponents. The expression (2x−7) is a polynomial, and understanding its behavior, including how to manipulate it through operations like division, is fundamental in algebra. This knowledge helps in recognizing the structure of the expression and applying the correct operations.
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Related Practice
Textbook Question
Factor completely, or state that the polynomial is prime.
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Textbook Question
Factor completely, or state that the polynomial is prime.
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Textbook Question
Evaluate each expression without using a calculator. 16-6/2
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Textbook Question
In Exercises 65–92, factor completely, or state that the polynomial is prime. x2y−16y+32−2x2
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Textbook Question
In Exercises 83–90, perform the indicated operations. Simplify the result, if possible.
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