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: 83

Answer

$y^{\frac{1}{2}}$

Work Step by Step

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