Textbook Question
Find each product. (x+5)(x−5)
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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 32
Simplify each exponential expression in Exercises 23–64.
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Identify the rule for simplifying expressions of the form \((a^m)^n\), which states that you multiply the exponents: \((a^m)^n = a^{m \times n}\).
Apply this rule to the given expression \((x^{11})^5\) by multiplying the exponents 11 and 5.
Write the expression with the new exponent: \(x^{11 \times 5}\).
Simplify the exponent multiplication to get \(x^{55}\).
Express the final simplified form as \(x^{55}\).
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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 raising a power to another power, you multiply the exponents. For example, (x^a)^b = x^(a*b). Understanding these laws is essential for simplifying expressions like (x^11)^5.
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Power of a Power Rule
The power of a power rule states that when an exponential expression is raised to another exponent, you multiply the exponents. This rule helps simplify expressions by reducing nested exponents into a single exponent, making calculations and further manipulations easier.
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Variable Exponents
Variable exponents involve expressions where the base is a variable raised to a power. Recognizing how to manipulate these exponents correctly, especially when combined with exponent rules, is crucial for simplifying algebraic expressions and solving related problems.
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Related Practice
Textbook Question
Add or subtract as indicated. (3x+2)/(3x+4) + (3x+6)/(3x+4)
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Textbook Question
Write each number in decimal notation: 7.45*10^(-5)
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Textbook Question
In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 9x2+5x−4
Textbook Question
Write each number in scientific notation. 3,590,000
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Textbook Question
In Exercises 15–32, multiply or divide as indicated. (x3−25x)/4x2 ⋅ (2x2−2)/(x2−6x+5) ÷ (x2+5x)/(7x+7)
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