Textbook Question
Find the union of the sets. {e,m,p,t,y} ∪ ∅
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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 35
Simplify each exponential expression in Exercises 23–64.
Verified step by step guidance1
Identify the rule for dividing exponential expressions with the same base: when dividing, subtract the exponents. This rule is written as \(\frac{a^m}{a^n} = a^{m-n}\).
Apply the rule to the given expression \(\frac{x^{14}}{x^{7}}\). Since the base is the same (x), subtract the exponent in the denominator from the exponent in the numerator.
Write the expression after subtracting the exponents: \(x^{14-7}\).
Simplify the exponent by performing the subtraction: \(14 - 7\).
Express the simplified form of the exponential expression as \(x^{7}\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Laws of Exponents
The laws of exponents provide rules for simplifying expressions involving powers. One key rule is that when dividing like bases, you subtract the exponents: a^m / a^n = a^(m-n). This rule helps simplify expressions such as x^14 / x^7 by subtracting the exponents 14 and 7.
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Simplifying Algebraic Expressions
Simplifying algebraic expressions involves reducing them to their simplest form by applying arithmetic and algebraic rules. In this case, simplifying x^14 / x^7 means rewriting the expression using exponent rules to make it easier to understand or use in further calculations.
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Properties of Variables and Exponents
Variables represent unknown or changing quantities, and exponents indicate repeated multiplication. Understanding how variables behave under exponentiation and division is essential to correctly simplify expressions like x^14 / x^7, ensuring the variable remains consistent while adjusting the exponent.
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Related Practice
Textbook Question
Add or subtract terms whenever possible.
Textbook Question
List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. {-9, -4/5, 0, 0.25, √3, 9.2, √100}
Textbook Question
Perform the indicated operation and write the answer in decimal notation.
Textbook Question
Find each product. (5−7x)(5+7x)
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Textbook Question
In Exercises 33–44, add or subtract terms whenever possible. 8√5+11√5
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