Power of a Power Property
Initial Definition

If "a" is a non-zero integer and "m" and "n" are whole numbers, then:


(am)n = amn


By the symmetric property of equality, this property can be written either way.

Product of Powers (Common Base) Property

Example/Explanation

(23)4 = (23)(23)(23)(23)                                [Definition of a power]


(23)4 = (2x2x2)(2x2x2)(2x2x2)(2x2x2)        [Definition of a power]


(23)4 = 2x2x2x2x2x2x2x2x2x2x2x2            [Definition of a power]


(23)4 = 212                                                  [Definition of a power]

Divider Line

Generalization


(am)n = amn