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: 6

Answer

The missing power is $\frac{2}{3}$.

Work Step by Step

RECALL: $a^m \cdot a^n = a^{m+n}$ Let x = missing/unknown power Use the rule above to obtain: $5^{\frac{1}{3}} \cdot 5^{x} = 5 \\5^{\frac{1}{3}} \cdot 5^{x} = 5^1 \\5^{\frac{1}{3}+x}=5^1$ Use the rule "If $a^x=a^y$, then $x=y$" to obtain: $\frac{1}{3} + x = 1 \\x = 1 - \frac{1}{3} \\x = \frac{3}{3} - \frac{1}{3} \\x = \frac{2}{3}$
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