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,...
Related questions
Question
Help!!
in case it's blurry it says
Sinplify the expression 3x-4y5/(2x3y-7)-2 and write the answer using only positive exponents
![To simplify the expression \(\frac{3x^{-1}y^5}{(2x^3y^{-1}z)^{-2}}\) and write the answer using only positive exponents, follow these steps:
1. **Simplify the Denominator**:
\((2x^3y^{-1}z)^{-2}\) means taking the reciprocal and squaring each factor:
\[
(2^{-2})(x^{-6})(y^2)(z^{-2}) = \frac{1}{4x^6y^2z^2}
\]
2. **Rewrite the Expression with Reciprocal**:
Replace the denominator with the expression derived:
\[
3x^{-1}y^5 \times 4x^6y^2z^2 = 12x^{-1+6}y^{5+2}z^2
\]
3. **Simplify Exponents**:
\[
12x^{5}y^{7}z^2
\]
Thus, the final simplified expression with only positive exponents is:
\[
12x^5y^7z^2
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47ebf8e0-0639-4c02-a098-1722152a8587%2F2b00f73b-c551-4102-8d3b-bbdd68dddc75%2F4bmdpke.jpeg&w=3840&q=75)
Transcribed Image Text:To simplify the expression \(\frac{3x^{-1}y^5}{(2x^3y^{-1}z)^{-2}}\) and write the answer using only positive exponents, follow these steps:
1. **Simplify the Denominator**:
\((2x^3y^{-1}z)^{-2}\) means taking the reciprocal and squaring each factor:
\[
(2^{-2})(x^{-6})(y^2)(z^{-2}) = \frac{1}{4x^6y^2z^2}
\]
2. **Rewrite the Expression with Reciprocal**:
Replace the denominator with the expression derived:
\[
3x^{-1}y^5 \times 4x^6y^2z^2 = 12x^{-1+6}y^{5+2}z^2
\]
3. **Simplify Exponents**:
\[
12x^{5}y^{7}z^2
\]
Thus, the final simplified expression with only positive exponents is:
\[
12x^5y^7z^2
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education