Rational Exponents
• Definition of 
If n is
a positive integer greater than 1 and 
is a
real number , then
Rewrite as a radical expression and simplify if possible.
• Definition of 
If m
and n are positive integers greater than 1 with
in simplest form , then
as long as 
is a real
number .
Use radical notation to rewrite each expression. Simplify if possible.
• Definition of 
as
long as 
is a nonzero real number.
Write each expression with a positive exponent. Then simplify.
• Summary of Exponent Rules
If m and n are rational numbers , and a, b, and c are numbers for which the
expressions below exist,
then
Product rule for exponents :
Power rule for exponents:
Power rules for products and quotients :
Quotient rule for exponents :
Use the properties of exponents to simplify .
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