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: 18



Work Step by Step

$$(\sqrt3)^{1/2}\times(\sqrt{12})^{1/2}$$ As $\sqrt3\gt0$ and $\sqrt{12}\gt0$, we can apply the law of exponents here. Applying this law: $$a^x\times b^x=(ab)^x$$ we have $$(\sqrt3)^{1/2}\times(\sqrt{12})^{1/2}=(\sqrt3\times\sqrt{12})^{1/2}=(\sqrt{36})^{1/2}=6^{1/2}=\sqrt6$$
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