Textbook Question
Write each number in scientific notation. 579,000,000,000,000,000
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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 80
State the name of the property illustrated. 7⋅(11⋅8)=(11⋅8)⋅7
Verified step by step guidance1
Identify the given expression: \(7 \cdot (11 \cdot 8) = (11 \cdot 8) \cdot 7\).
Notice that the grouping of the numbers changes from \(7\) multiplied by the product of \(11\) and \(8\), to the product of \(11\) and \(8\) multiplied by \(7\).
Observe that the order of the numbers is also changed, but the multiplication operation remains the same.
Recall that the Commutative Property of Multiplication states that changing the order of factors does not change the product: \(a \cdot b = b \cdot a\).
Therefore, this equation illustrates the Commutative Property of Multiplication because the factors are rearranged but the product remains unchanged.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Associative Property of Multiplication
This property states that when multiplying three or more numbers, the way in which the numbers are grouped does not affect the product. For example, (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c). It focuses on the grouping of factors, not their order.
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Change of Base Property
Commutative Property of Multiplication
This property states that the order of factors can be changed without affecting the product. For example, a ⋅ b = b ⋅ a. It emphasizes that multiplication is independent of the sequence of numbers.
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5:36Change of Base Property
Understanding Mathematical Notation and Grouping Symbols
Parentheses indicate the grouping of numbers or operations to be performed first. Recognizing how parentheses affect the order of operations is essential to identify properties like associative or commutative in expressions.
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06:08End Behavior of Polynomial Functions
Related Practice
Textbook Question
In Exercises 65–92, factor completely, or state that the polynomial is prime. x3+2x2−4x−8
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Textbook Question
In Exercises 69–82, simplify each complex rational expression. (1/(x+h)2 − 1/x2)/h
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Textbook Question
Perform the indicated operations. Indicate the degree of the resulting polynomial.
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Textbook Question
In Exercises 67–82, find each product. (7xy2−10y)(7xy2+10y)
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Textbook Question
In Exercises 75–82, add or subtract terms whenever possible. ³√54xy3−y³√128x
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