College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.2 - Algebra Essentials - R.2 Assess Your Understanding - Page 27: 91



Work Step by Step

RECALL: (1) $(a^m)^n=a^{mn}$ (2) $(ab)^m=a^mb^m$ (3) $a^{-m} = \dfrac{1}{a^m}, a \ne 0$ (4) $\dfrac{a^m}{a^n} = a^{m-n}$ (5) $a^1 = a$ Use rule (4) above to obtain: $=\dfrac{x^2}{x} \cdot \dfrac{y^3}{y^4} \\=x^{2-1} \cdot y^{3-4} \\=x^1 \cdot y^{-1}$ Use rule (5) to obtain: $\\=x \cdot y^{-1}$ Use rule (3) above to obtain: $=x \cdot \frac{1}{y^1} \\=x \cdot \frac{1}{y} \\=\dfrac{x}{y}$
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