College Algebra 7th Edition

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

Chapter P, Prerequisites - Section P.4 - Rational Exponents and Radicals - P.4 Exercises - Page 30: 76



Work Step by Step

RECALL: (i) $a^{-m} = \dfrac{1}{a^m}$ (ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ (iii) $a^m \cdot a^n = a^{m+n}$ Use rule (ii) above to obtain: $=2a^{\frac{1}{2}} \cdot a^{\frac{2}{3}} \\=2\cdot a^{\frac{1}{2}}\cdot a^{\frac{2}{3}}$ Use rule (iii) above to to obtain: $=2\cdot a^{\frac{1}{2} + \frac{2}{3}} \\=2a^{\frac{3}{6} + \frac{4}{6}} \\=2a^{\frac{7}{6}}$
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