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Properties of Exponents

From the basic definition of positive integer exponents, we have

(1)
$ a^{n_1} a^{n_2} = a^{n_1 + n_2}$
(2)
$ \left(a^{n_1}\right)^{n_2} = a^{n_1 n_2}$
Note that property (1) implies property (2). We list them both explicitly for convenience below.


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``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-04-06 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA