Elementary Algebra

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

Chapter 11 - Additional Topics - Chapter 11 Review Problem Set: 31

Answer

$\frac{1}{3}$

Work Step by Step

We start with the given expression: $\frac{3^{1/3}}{3^{4/3}}$ To divide powers with the same base, we subtract the exponents: $3^{(1/3)-(4/3)}=3^{-3/3}=3^{-1}$ The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$ We use this rule to rewrite the expression: $\frac{1}{3^1}=\frac{1}{3}$
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