Rules for Exponents
One as an Exponent: Anything to the power of one
is itself.
a1  a
Product to Power: When raising a product to a
power, raise each factor to the power.
3b2  9b2
abm  a mb m
51  5
Quotient to Power: When raising a quotient to a
Zero as an Exponent: Anything to the power of zero power, raise the numerator and denominator to the
is one.
power.
m
a0  1
3650  1
Product Rule: When multiplying expressions with
like bases add the exponents.
a a  a
m
n
m n
2  2  2  256
3
5
8
Power Rule: When taking a power to a power
multiply the exponents.
a 
m n
 a mn
Tri-County Technical College
3 
2 3
3
am
a
   m
b
b
23
8
2
   3 
5
125
5
Quotient Rule: When dividing expressions with like
base subtract the exponents.
am
 a mn
n
a
610
 6 2  36
8
6
Negative Exponents: When getting rid of negative
exponents switch places.
 3  729
6
a
May 2006
n
1
 n
a
8
2
1
1
 2 
8
64
1
42

 16
4 2
1
Created by Tonia Faulling