Textbook Question
State the name of the property illustrated: (6 • 3) • 9 = 6 • (3 • 9)
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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 13
Evaluate each exponential expression in Exercises 1–22.
Verified step by step guidance1
Identify the properties of exponents that apply to the expression \(2^2 \cdot 2^3\). Since the bases are the same (both are 2), you can use the product of powers property.
Recall the product of powers property: \(a^m \cdot a^n = a^{m+n}\). This means you add the exponents when multiplying with the same base.
Apply the property to the given expression: \(2^2 \cdot 2^3 = 2^{2+3}\).
Simplify the exponent by adding: \(2^{2+3} = 2^5\).
Express the final exponential form as \$2^5$, which is the simplified form of the original expression.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Properties of Exponents
This concept involves the rules that govern how to manipulate expressions with exponents. For example, when multiplying powers with the same base, you add the exponents: a^m * a^n = a^(m+n). Understanding these properties is essential for simplifying exponential expressions.
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04:06
Rational Exponents
Base and Exponent
An exponential expression consists of a base and an exponent, where the base is the number being multiplied, and the exponent indicates how many times the base is used as a factor. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 multiplied by itself three times.
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7:39Introduction to Exponent Rules
Evaluating Exponential Expressions
Evaluating an exponential expression means calculating its numerical value by performing the repeated multiplication indicated by the exponent. For instance, 2^3 equals 2 × 2 × 2 = 8. This step is necessary to find the final value of expressions like 2^2 * 2^3.
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03:11Evaluating Algebraic Expressions
Related Practice
Textbook Question
Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √27
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Textbook Question
State the name of the property illustrated: 3+17 = 17+3
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Textbook Question
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (5x2−7x−8)+(2x2−3x+7)−(x2−4x−3)
Textbook Question
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (x2−14x+49)/(x2−49)
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Textbook Question
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 5(x+2)/(2x-14), for x=10
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