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(32-3 625"+¹ = 125-2n 5-3v-1 - 53v = 22-x. 2-2-2-2² = 2x

(32-3 625"+¹ = 125-2n 5-3v-1 - 53v = 22-x. 2-2-2-2² = 2x

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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None of these problems require using logarithms to solve.  Which problem seems the easiest to solve?  Which one seems like the most complicated?

Certainly! Here is the transcription and explanation of the mathematical expressions in the image: --- **Mathematical Expressions:** 1. \( \left(\frac{1}{5}\right)^{3n - 3} \cdot 625^{n+1} = 125^{-2n} \) - This expression involves powers of fractions and integers. It equates a product of a fraction raised to a power and an integer raised to a power with another integer raised to a negative power. 2. \( 5^{-3v-1} = 5^{3v} \) - In this equation, powers of 5 are equated. The equation shows that one form of an exponent can be transformed or simplified into another. 3. \( 2^{2-x} \cdot 2^{-2x-2} = 2^{2x} \) - This expression utilizes properties of exponents to equate two different products of powers of 2 to a single power of 2. --- **Explanation:** These expressions demonstrate the use of exponent rules in algebra. The problems can be used to help understand: - Simplifying expressions with exponents. - The property of exponents where \((a^m \cdot a^n = a^{m+n})\). - Solving equations that involve matching exponents to determine the values of variables. These exercises are commonly used in algebra to test understanding of exponent rules and their applications in simplifying and solving equations.
Transcribed Image Text:Certainly! Here is the transcription and explanation of the mathematical expressions in the image: --- **Mathematical Expressions:** 1. \( \left(\frac{1}{5}\right)^{3n - 3} \cdot 625^{n+1} = 125^{-2n} \) - This expression involves powers of fractions and integers. It equates a product of a fraction raised to a power and an integer raised to a power with another integer raised to a negative power. 2. \( 5^{-3v-1} = 5^{3v} \) - In this equation, powers of 5 are equated. The equation shows that one form of an exponent can be transformed or simplified into another. 3. \( 2^{2-x} \cdot 2^{-2x-2} = 2^{2x} \) - This expression utilizes properties of exponents to equate two different products of powers of 2 to a single power of 2. --- **Explanation:** These expressions demonstrate the use of exponent rules in algebra. The problems can be used to help understand: - Simplifying expressions with exponents. - The property of exponents where \((a^m \cdot a^n = a^{m+n})\). - Solving equations that involve matching exponents to determine the values of variables. These exercises are commonly used in algebra to test understanding of exponent rules and their applications in simplifying and solving equations.
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