Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Review: 27

Answer

$\frac{1}{3}$

Work Step by Step

Step 1: We need to transform 81 into a number of power 4 so that exponential powers can cancel each other out Step 2: We find that $81=3^{4}$ Step 3: Therefore, we can write $(\frac{1}{81})^{\frac{1}{4}}$ as $(\frac{1}{3^{4}})^{\frac{1}{4}}$ Step 4: $(\frac{1}{3^{4}})^{\frac{1}{4}}$= $\frac{1^{\frac{1}{4}}}{3^{4\times\frac{1}{4}}}$ Step 5: $1^{\frac{1}{4}}$=$ 1$ and ${3^{4\times\frac{1}{4}}}$=$3$ as both 4s cancel each other out Step 6: Therefore, what remains is $\frac{1}{3}$
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