Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.6 Rational Exponents - R.6 Exercises: 6

Answer

False Correct Statement: $m^{2/3} \cdot m^{1/3} = m$

Work Step by Step

RECALL: (1) $a^{-m} = \dfrac{1}{a^m}$ (2) $\dfrac{a^m}{a^n} = a^{m-n}$ (3) $a^1=a$ (4) $a^m\cdot a^n = a^{m+n}$ Use rule (4) above to obtain: $m^{2/3} \cdot m^{1/3}=m^{2/3+1/3}=m^1=m$ Thus, the given statement is false. The correct statement is: $m^{2/1} \cdot m^{1/3} = m$
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