Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises: 108

Answer

$(b^{x})^{y}=b^{xy}$ This is known as third Law of Exponents; where x and y are real numbers.

Work Step by Step

We already know that $lnb^{r}=rlnb$ Now, $(b^{x})^{y}=e^{yln(b^{x})}$ Also, $b^{x}=e^{xlnb}$ This implies $e^{yxlnb}=e^{xylnb}$ Hence, $(b^{x})^{y}=b^{xy}$ This is known as third Law of Exponents; where x and y are real numbers.
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