College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.7 - Radical Expressions - R.7 Exercises: 67

Answer

$\sqrt[12]{2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Convert the given expression, $ \sqrt[4]{\sqrt[3]{2}} ,$ in exponential form by using the definition of rational exponents. Then use the laws of exponents to simplify the exponent. Finally, use the definition of rational exponents again to express the answer in radical form. $\bf{\text{Solution Details:}}$ Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt[4]{2^{\frac{1}{3}}} \\\\= \left(2^{\frac{1}{3}}\right)^{\frac{1}{4}} .\end{array} Using the Power Rule of the laws of exponents which is given by $\left( x^m \right)^p=x^{mp},$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2^{\frac{1}{3}\cdot\frac{1}{4}} \\\\= 2^{\frac{1}{12}} \\\\= \sqrt[12]{2^{1}} \\\\= \sqrt[12]{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.