Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 4 - Chapters R-4 - Cumulative Review Exercises: 29

Answer

$\dfrac{y^{7}}{x^{13}z^{2}}$

Work Step by Step

Use the laws of exponents to simplify the given expression, $ \dfrac{x^{-6}y^3z^{-1}}{x^7y^{-4}z} .$ Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the quotient of the expression above is \begin{array}{l}\require{cancel} x^{-6-7}y^{3-(-4)}z^{-1-1} \\\\= x^{-6-7}y^{3+4}z^{-1-1} \\\\= x^{-13}y^{7}z^{-2} .\end{array} Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{y^{7}}{x^{13}z^{2}} .\end{array}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.