University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.5 - Exponential Functions - Exercises - Page 38: 16



Work Step by Step

$$(13^{\sqrt2})^{\sqrt2/2}$$ As $13\gt0$, we can apply the law of exponents here. Applying this law: $$(a^x)^y=a^{xy}$$ we have $$(13^{\sqrt2})^{\sqrt2/2}=13^{[\sqrt2\times\frac{\sqrt2}{2}]}=13^{2/2}=13^1=13$$
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