Homework Help is Here – Start Your Trial Now!
Math
Algebra
491. x ³x4 -3 492. 56 58 493. (47a¹86235) 0 494. 4-¹ -1

491. x ³x4 -3 492. 56 58 493. (47a¹86235) 0 494. 4-¹ -1

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,...
See similar textbooks
icon
Related questions
Question
491,492,493，494
Here is a transcription and explanation of the mathematical expressions displayed in the image, which will be useful for educational purposes focused on exponents and algebraic expressions. 491. \( x^3 \cdot x^4 \) 492. \( \frac{5^6}{5^8} \) 493. \( (47a^{18}b^{23}c^5)^0 \) 494. \( 4^{-1} \) 495. \( (2y)^{-3} \) 496. \( p^{-3} \cdot p^8 \) 497. \( \frac{x^4}{x^5} \) 498. \( (3x^{-3})^2 \) 499. \( \frac{24r^3s^5}{6r^2s^7} \) 500. \( \left(\frac{x^4y^9}{x^3}\right)^2 \) ### Explanation of Expressions: 1. **Simplifying Exponents:** - Problems like 491, 496, and 497 involve using properties of exponents to simplify expressions. For example, in 491, when multiplying like bases, you add the exponents. 2. **Power of a Power:** - Problems like 493 and 495 involve applying the power of a power property, where you multiply the exponents. 3. **Negative Exponents:** - Problems 494, 495, and 498 involve expressions with negative exponents. These should be rewritten as fractions to simplify. 4. **Division of Exponents:** - Problems 492 and 497 involve dividing expressions with the same base, requiring subtracting the exponents. 5. **Complex Fractions:** - Problem 499 involves both division of coefficients and application of exponent rules when simplifying a fraction. These problems are representative examples of applying exponent rules in algebra. Understanding how to manipulate exponents is crucial for simplifying complex algebraic expressions.
Transcribed Image Text:Here is a transcription and explanation of the mathematical expressions displayed in the image, which will be useful for educational purposes focused on exponents and algebraic expressions. 491. \( x^3 \cdot x^4 \) 492. \( \frac{5^6}{5^8} \) 493. \( (47a^{18}b^{23}c^5)^0 \) 494. \( 4^{-1} \) 495. \( (2y)^{-3} \) 496. \( p^{-3} \cdot p^8 \) 497. \( \frac{x^4}{x^5} \) 498. \( (3x^{-3})^2 \) 499. \( \frac{24r^3s^5}{6r^2s^7} \) 500. \( \left(\frac{x^4y^9}{x^3}\right)^2 \) ### Explanation of Expressions: 1. **Simplifying Exponents:** - Problems like 491, 496, and 497 involve using properties of exponents to simplify expressions. For example, in 491, when multiplying like bases, you add the exponents. 2. **Power of a Power:** - Problems like 493 and 495 involve applying the power of a power property, where you multiply the exponents. 3. **Negative Exponents:** - Problems 494, 495, and 498 involve expressions with negative exponents. These should be rewritten as fractions to simplify. 4. **Division of Exponents:** - Problems 492 and 497 involve dividing expressions with the same base, requiring subtracting the exponents. 5. **Complex Fractions:** - Problem 499 involves both division of coefficients and application of exponent rules when simplifying a fraction. These problems are representative examples of applying exponent rules in algebra. Understanding how to manipulate exponents is crucial for simplifying complex algebraic expressions.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS