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 7.2 - Rational Exponents - Exercise Set: 78

Answer

$16y^{\frac{1}{2}}$

Work Step by Step

RECALL: (1) $a^m \cdot a^n = a^{m+n}$ (2) $\dfrac{a^m}{a^n} = a^{m-n}$ (3) $(ab)^m =a^mb^m$ Use rule (3) above to obtain: $=\dfrac{2^4(y^{\frac{1}{5}})^4}{y^{\frac{3}{10}}} \\=\dfrac{2(2)(2)(2)(y^{\frac{1}{5}})^4}{y^{\frac{3}{10}}} \\=\dfrac{16(y^{\frac{1}{5}})^4}{y^{\frac{3}{10}}}$ Use rule (3) above to obtain: $=\dfrac{16(y^{\frac{1}{5}(4)})}{y^{\frac{3}{10}}} \\=\dfrac{16y^{\frac{4}{5}}}{y^{\frac{3}{10}}}$ Use rule (2) above to obtain: $=16 y^{\frac{4}{5} - \frac{3}{10}}$ Make the fractional exponents similar using their LCD of $10$ to obtain: $=16 y^{\frac{8}{10} - \frac{3}{10}} \\=16 y^{\frac{8-3}{10}} \\=16 y^{\frac{5}{10}} \\=16y^{\frac{1}{2}}$
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