Math Resources
Exponent Rules
LIKE TERMS AND EXPONENTS.
. . . . . .Everything you ever wanted to know, but were afraid to ask!
Math Idea
Formal Statement
Like
Terms
Like terms must have the
following:
a) the same combination
of variables
b) the same combination
of exponents on those
variables
c) or they can be constants
*Only like terms can be added
and/or subtracted.
** When you add or subtract
like terms, do not change the
exponents!
***You can multiply any
polynomials you like, whether
they are alike or not!!
Multiplying
Monomials
Product
Rule
When you multiply monomials
with the same base, just add the
exponents and keep the base!
The Learning Center of RCC
Common Sense Fact
When you add three four door
cars and six four door cars you
don’t get nine eight door cars –
you just get nine four door
cars! The things that you are
adding do not change, just the
number of those things that
you have.
When you write the terms,
often you can see the
exponents horizontally across
from one another – so you
could draw a big plus sign
between them. Remember
that the numbers in the front
(AKA the coefficients) are still
multiplied.
The bases are the SAME!
General Example 1
x  x  2x
n
n
Example 2
3x 2 y 3  6x  5x 2 y 3  7x 
n
8x 2 y 3  x
a x ga y  a x  y
5x 2 yg2xy 4  10x 3 y5
Created by A McNeill
Math Resources
Raising a
Monomial
to Power
Power
Rule
Exponent Rules
When you raise a monomial term
to some power, multiply the
exponents
When you divide two monomial
terms with the same base subtract
the exponents, and keep the base!
Dividing a
Monomial
by a
Monomial
Quotient
Rule
The Learning Center of RCC
When you write the
monomial it is inside
parentheses and the
exponent is outside of the
parentheses and this could
serve as a reminder to you
to multiply them. Note that
the coefficients are raised to
the power as well!
When you divide
monomials, always
remember to divide the
coefficients or reduce them
to their lowest terms. Note
that when you subtract your
exponents that your base
will always end up where
the larger exponent is
located. If the larger
exponent is in the
numerator, subtract the
exponents and write your
base and the new exponent
(the difference) in the
numerator. If the larger
exponent is in the
denominator, then subtract
and place your base and the
new exponent in the
denominator!
a   a
m n
6x y z  
6 (x ) y  z 
3 2 4 2
mgn
 a mn
2
3 2
2 2
4 2
36x 6 y 4 z 8
28x 8 y5 4x 5

35x 3 y 7 5y2
am
m n

a
an
Created by A McNeill
Math Resources
Zero
Exponent
Rule
Exponent Rules
When you raise anything to the
zero power the answer is 1!
When you have a power of
0, it is telling you that you
have none of that base – you
only have the “understood”
coefficient 1. So since you
have none of that base all
you have left is the
coefficient 1.
Also consider the quotient
rule and note the following:
2
x
1
x2
x22  1
6x 0  1
a 1
0
x0  1
Negative
Exponent
Rule
Fractions
Raised to
Negative
Exponents
When you raise any base to a
negative exponent ; it is the same
as raising the reciprocal of that
base to the positive exponent!
When you raise a fraction to a
negative exponent, write the
reciprocal of the fraction and write
the positive exponent
The Learning Center of RCC
When you have a negative
exponent, it creates a
reciprocal; by flipping the
current base over and
replacing the negative
exponent with a positive
exponent. Be careful that
you notice which numbers
and terms are being raised
to the negative exponents
and which ones are not!
When your base is a
fraction, flip the fraction
(write its reciprocal) then
apply the positive exponent
to the numerator and the
denominator .
1
an
1
an

n
a
1
an 
 a
 
b
n
 b
 
 a
2
3 4
6x y z
n
 7x 2 
 6y 
3
6y 3
 2 4
x z
 6y 
 2
 7x 
3
63 y3
216y 3

7 3 (x 2 )3 343x 6
Created by A McNeill
Math Resources
The Learning Center of RCC
Exponent Rules
Created by A McNeill