Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - Mid-Chapter Review - Mixed Review - Page 663: 17



Work Step by Step

Using $x^{m/n}=\sqrt[n]{x^m}=\left(\sqrt[n]{x} \right)^m,$ then \begin{array}{l}\require{cancel} \dfrac{\sqrt{t}}{\sqrt[8]{t^3}} \\\\= \dfrac{t^{1/2}}{t^{3/8}} .\end{array} Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to \begin{array}{l}\require{cancel} \dfrac{t^{1/2}}{t^{3/8}} \\\\= t^{\frac{1}{2}-\frac{3}{8}} \\\\= t^{\frac{4}{8}-\frac{3}{8}} \\\\= t^{\frac{1}{8}} .\end{array} Using $x^{m/n}=\sqrt[n]{x^m}=\left(\sqrt[n]{x} \right)^m,$ then \begin{array}{l}\require{cancel} t^{\frac{1}{8}} \\\\= \sqrt[8]{t^1} \\\\= \sqrt[8]{t} .\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.