For all real numbers n, m, x, y Exponent Properties For all real numbers n, m, x, y (except that 00 is undefined, and denominators can never be zero)

Exponent Properties

Exponent Properties Warning

Derivations We know that n factors If n is a positive integer

Derivations Consider when n > m For Example: So adopt the rule:

Derivations Now suppose n = m But we know that So it must be true that

Derivations Now suppose n < m, for example: But our rule says So we must conclude that

Derivations Or in general, And by extension