Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.3 - Fractional Exponents - Concept Quiz 11.3 - Page 489: 5



Work Step by Step

We simplify both the expressions to see if they are equivalent or not: $\sqrt[n] {x^{m}}=(x^{m})^{\frac{1}{n}}=x^{\frac{m}{n}}$ $(\sqrt[n] x)^{m}=(x^{\frac{1}{n}})^{m}=x^{\frac{1}{n}\times m}=x^{\frac{m}{n}}$ Therefore, the two expressions are equivalent and the question statement is true.
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