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.