Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set: 124

Answer

$p^{2}qr^{11}\sqrt[4] (p^{3}r)$

Work Step by Step

$\sqrt[4] (p^{11}q^{4}r^{45})=\sqrt[4] (p^{8}\times q^{4}\times r^{44}\times p^{3}r)=\sqrt[4] (p^{8})\times \sqrt[4] (q^{4}) \times \sqrt[4] (r^{44})\times \sqrt[4] (p^{3}r)=p^{2}qr^{11}\sqrt[4] (p^{3}r)$ $\sqrt[4] (p^{8})=p^{2}$, because $(p^{2})^{4}=p^{2\times4}=p^{8}$ $\sqrt[4] (q^{4})=q$, because $(q)^{4}=q^{4}$ $\sqrt[4] (r^{44})=r^{11}$, because $(r^{11})^{4}=r^{11\times4}=r^{44}$
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