College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.1 - Exponential Functions - 4.1 Exercises: 1

Answer

$5^{\frac{1}{3}}$

Work Step by Step

For any rational exponent $\frac{1}{n}$, where $n>0$, we say that $a^{\frac{1}{n}}=\sqrt[n] a$. That is, we can rewrite a rational exponent as a root and vice versa. In the expression $\sqrt[3] 5$, we see that 5 is in the place of a and 3 is in the place of n. Using the equivalency above, we can rearrange the root into the exponential notation, $5^{\frac{1}{3}}$.
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