Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.4 - Adding, Subtracting, and Dividing Radical Expressions - Exercise Set: 55

Answer

$4a^5b^5$

Work Step by Step

RECALL: (1) The quotient rule: $\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}}$ where $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers and $b\ne0$ (2) $\dfrac{a^m}{a^n} = a^{m-n}, a \ne 0$ Use the quotient rule above to obtain: $\require{cancel}=\sqrt{\dfrac{48a^8b^7}{3a^{-2}b^{-3}}} \\=\sqrt{\dfrac{16\cancel{48}a^8b^7}{\cancel{3}a^{-2}b^{-3}}} \\=\sqrt{\dfrac{16a^8b^7}{a^{-2}b^{-3}}}$ Use rule (2) above to obtain: $=\\=\sqrt{16a^{8-(-2)}b^{7-(-3)}} \\=\sqrt{16a^{8+2}b^{7+3}} \\=\sqrt{16a^{10}b^{10}}$ Factor the radicand so that at least one factor is a perfect square to obtain: $=\sqrt{(4a^5b^5)^2}$ Simplify to obtain: $=4a^5b^5$
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