Using the laws of exponents, we can derive what fractional and
negative powers mean:
a0=a1−1=a1a1=1, as
long as a≠0.
a−n=a0−n=a0an=1an, as long as a≠0.
(ap/q)q=ap, so
ap/q=q√ap=(q√a)p,
as long as a≥0.
Notice: the expression
00, as well as negative powers of 0 are not
defined, and neither are fractional powers of
negative numbers, since if a<0, ap will not have a (real)
q-th root.
DO:
You must know all the exponential rules, so please review and
work on this and the previous slide if you have not totally
mastered these rules.