information:classification, information:filtering
Identities and properties

The following identities, often called exponent rules, hold for all integer exponents, provided that the base is non-zero:

Unlike addition and multiplication, exponentiation is not commutative. For example, 2 = 8 ≠ 3 = 9. Also unlike addition and multiplication, exponentiation is not associative. For example, (2) = 8 = 64, whereas 2 = 2 = 512. Without parentheses, the conventional order of operations for serial exponentiation in superscript notation is top-down (or right -associative), not bottom-up (or left -associative). That is,

which, in general, is different from