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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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Positive Integer Exponents