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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Question
![**Exercise 3.** Simplify as much as possible and write the final answer only with positive exponents.
\[
\frac{\left( 4y^{-1} \right)^{-2}}{\left( x^{-2} \right)^{-1}} \left( 4xy^{-1} \right)^{2}
\]
**Explanation:**
This exercise involves simplifying an expression with both negative and positive exponents. The main goal is to manipulate the expression so that all exponents are positive in the final result.
Here's a breakdown of what each part represents:
- The numerator consists of the expression \((4y^{-1})^{-2}\), which has both a negative exponent outside and inside the parentheses.
- The denominator is \((x^{-2})^{-1}\), with a negative exponent both inside and outside the parentheses.
- The last term outside the fraction is multiplied by the fraction: \((4xy^{-1})^{2}\), which implies that both \(x\) and \(y^{-1}\) are raised to the power of 2.
To solve the exercise, you'll need to apply the laws of exponents, such as:
- \((a^m)^n = a^{m \cdot n}\)
- \(a^{-m} = \frac{1}{a^m}\)
- \(\frac{a^m}{a^n} = a^{m-n}\)
Work through each component, simplify step-by-step, and ensure all exponents are positive in your final answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb88d9b02-73da-424d-af4e-50ad976cc081%2F107a7a4b-6e9e-47ab-8e0a-3b97950d6062%2Fbss3w3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 3.** Simplify as much as possible and write the final answer only with positive exponents.
\[
\frac{\left( 4y^{-1} \right)^{-2}}{\left( x^{-2} \right)^{-1}} \left( 4xy^{-1} \right)^{2}
\]
**Explanation:**
This exercise involves simplifying an expression with both negative and positive exponents. The main goal is to manipulate the expression so that all exponents are positive in the final result.
Here's a breakdown of what each part represents:
- The numerator consists of the expression \((4y^{-1})^{-2}\), which has both a negative exponent outside and inside the parentheses.
- The denominator is \((x^{-2})^{-1}\), with a negative exponent both inside and outside the parentheses.
- The last term outside the fraction is multiplied by the fraction: \((4xy^{-1})^{2}\), which implies that both \(x\) and \(y^{-1}\) are raised to the power of 2.
To solve the exercise, you'll need to apply the laws of exponents, such as:
- \((a^m)^n = a^{m \cdot n}\)
- \(a^{-m} = \frac{1}{a^m}\)
- \(\frac{a^m}{a^n} = a^{m-n}\)
Work through each component, simplify step-by-step, and ensure all exponents are positive in your final answer.
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