MATH 11011 RATIONAL EXPONENTS KSU
Definition:
•Rational exponent: If mand nare positive integers with m/n in lowest terms, then
am/n =n
√am=¡n
√a¢m.
(If nis even then we require a≥0.) In other words, in a rational exponent, the numerator indicates
the power and the denominator indicates the root. For example,
82/3=³3
√8´2
= (2)2= 4.
Integer Exponent Rules:
•Product Rule: For any real numbers mand n,
am·an=am+n.
When multiplying like bases, we add the exponents.
•Quotient Rule: For any nonzero number aand any real numbers mand n,
am
an=am−n.
When we divide like bases, we subtract the exponents.
•Power Rule: For any real numbers mand n,
(am)n=amn.
When we raise a power to another power, we multiply the exponents.
•For any real number m,
(ab)m=am·bm.
When we have a product raised to a power, we raise each factor to the power.
•For any real number m,
³a
b´m=am
bm.
When we have a quotient raised to a power, we raise both the numerator and denominator to the
power.
