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Lesson: Exponents Quick Guide
Contributed by: Pappal
There are four operations you have to be able to do
There are four operations you have to be able to do
with exponents
There are four operations you have to be able to do
with exponents
Addition/Subtraction
There are four operations you have to be able to do
with exponents
Multiplication/Division
Addition/Subtraction
There are four operations you have to be able to do
with exponents
Exponents to Exponents
Multiplication/Division
Addition/Subtraction
There are four operations you have to be able to do
with exponents
Exponents to Exponents
Negative exponents
Multiplication/Division
Addition/Subtraction
First, addition and subtraction
First, addition and subtraction
To add or subtract terms, they must be
First, addition and subtraction
To add or subtract terms, they must be
'like terms'
Like terms have to have the same letter
First, addition and subtraction
To add or subtract terms, they must be
'like terms'
Like terms have to have the same letter
First, addition and subtraction
To add or subtract terms, they must be
2x2           3x2
'like terms'
Like terms have to have the same letter
First, addition and subtraction
To add or subtract terms, they must be
2x2           3x2
'like terms'
same letter
Like terms have to have the same letter
and those letter have to have the same exponents
First, addition and subtraction
To add or subtract terms, they must be
2x2           3x2
'like terms'
Like terms have to have the same letter
and those letter have to have the same exponents
First, addition and subtraction
To add or subtract terms, they must be
2x2           3x2
'like terms'
same exponents
then they can be added or subtracted
Like terms have to have the same letter
and those letter have to have the same exponents
First, addition and subtraction
To add or subtract terms, they must be
2x2           3x2
'like terms'
same exponents
then they can be added or subtracted
Like terms have to have the same letter
and those letter have to have the same exponents
First, addition and subtraction
To add or subtract terms, they must be
2x2           3x2
'like terms'
same exponents
2x2
then they can be added or subtracted
Like terms have to have the same letter
and those letter have to have the same exponents
First, addition and subtraction
To add or subtract terms, they must be
2x2           3x2
'like terms'
same exponents
2x2 +
then they can be added or subtracted
Like terms have to have the same letter
and those letter have to have the same exponents
First, addition and subtraction
To add or subtract terms, they must be
2x2           3x2
'like terms'
same exponents
2x2 + 3x2
then they can be added or subtracted
Like terms have to have the same letter
and those letter have to have the same exponents
First, addition and subtraction
To add or subtract terms, they must be
2x2           3x2
'like terms'
same exponents
2x2 + 3x2 =
then they can be added or subtracted
Like terms have to have the same letter
and those letter have to have the same exponents
First, addition and subtraction
To add or subtract terms, they must be
2x2           3x2
'like terms'
same exponents
2x2 + 3x2 = 5x2
Notice that when we add/subtract like terms
Notice that when we add/subtract like terms
the exponent doesn't change
Notice that when we add/subtract like terms
the exponent doesn't change
4x2
Notice that when we add/subtract like terms
the exponent doesn't change
4x2 +
Notice that when we add/subtract like terms
the exponent doesn't change
4x2 + 3x2
Notice that when we add/subtract like terms
the exponent doesn't change
4x2 + 3x2 =
Notice that when we add/subtract like terms
the exponent doesn't change
4x2 + 3x2 = 7x2
Notice that when we add/subtract like terms
the exponent doesn't change
4x2 + 3x2 = 7x2
Same exponents
10x3 + 4x3 =
x
-5x4 + 7x4 =
x
Which of these are like terms?
Unlike Terms
?
4x3 , 2x5
Like Terms
?
2x2 , 3x2
When multiplying terms with the same base
When multiplying terms with the same base
(x2)
When multiplying terms with the same base
(x2)(x3)
When multiplying terms with the same base
(x2)(x3)
same base
When multiplying terms with the same base
just add the exponents
(x2)(x3)
When multiplying terms with the same base
just add the exponents
(x2)(x3) =
When multiplying terms with the same base
just add the exponents
(x2)(x3) = x
When multiplying terms with the same base
just add the exponents
(x2)(x3) = x2
When multiplying terms with the same base
just add the exponents
(x2)(x3) = x2+
When multiplying terms with the same base
just add the exponents
(x2)(x3) = x2+3
When multiplying terms with the same base
just add the exponents
(x2)(x3) = x2+3 =
When multiplying terms with the same base
just add the exponents
(x2)(x3) = x2+3 = x5
When multiplying terms with the same base
just add the exponents
2x2
When multiplying terms with the same base
just add the exponents
2x2
When multiplying terms with the same base
just add the exponents
2x2•4x3
When multiplying terms with the same base
just add the exponents
2x2•4x3 =
When multiplying terms with the same base
just add the exponents
2x2•4x3 = 8x5
5x3 • 4x7 =
x
3x4 • x =
x
When dividing variables with exponents
When dividing variables with exponents
subtract the exponents
When dividing variables with exponents
subtract the exponents
x5
When dividing variables with exponents
subtract the exponents
x5
When dividing variables with exponents
subtract the exponents
x3
x5
When dividing variables with exponents
subtract the exponents
x3
x5
=
When dividing variables with exponents
subtract the exponents
x3
x5
=
x
When dividing variables with exponents
subtract the exponents
x3
x5
=
x5
When dividing variables with exponents
subtract the exponents
x3
x5
=
x5-
When dividing variables with exponents
subtract the exponents
x3
x5
=
x5-3
When dividing variables with exponents
subtract the exponents
x3
x5
=
x5-3
=
When dividing variables with exponents
subtract the exponents
x3
x5
=
x5-3
=
x2
When dividing variables with exponents
notice we use top minus bottom
subtract the exponents
x3
x5
=
x5-3
=
x2
When dividing variables with exponents
notice we use top minus bottom
subtract the exponents
x3
x5
=
top
x5-3
=
x2
When dividing variables with exponents
notice we use top minus bottom
subtract the exponents
x3
x5
=
top
bottom
x5-3
=
x2
When dividing variables with exponents
subtract the exponents
x5
x3
When dividing variables with exponents
subtract the exponents
x5
x3
=
When dividing variables with exponents
subtract the exponents
x5
x3
=
x3
When dividing variables with exponents
subtract the exponents
x5
x3
=
x3-
When dividing variables with exponents
subtract the exponents
x5
x3
=
x3-5
When dividing variables with exponents
subtract the exponents
x5
x3
=
x3-5
=
When dividing variables with exponents
subtract the exponents
x5
x3
=
x3-5
=
x-2
Since the exponent is negative
When dividing variables with exponents
subtract the exponents
x5
x3
=
x3-5
=
x-2
Since the exponent is negative
When dividing variables with exponents
subtract the exponents
x5
x3
=
x3-5
=
x-2
Negative exponent
Since the exponent is negative
When dividing variables with exponents
the x moves to the denominator
subtract the exponents
x5
x3
=
x3-5
=
x-2
Since the exponent is negative
When dividing variables with exponents
the x moves to the denominator
subtract the exponents
x5
x3
=
x3-5
=
x-2
1
denominator
Since the exponent is negative
When dividing variables with exponents
the x moves to the denominator
and the exponent becomes negative
subtract the exponents
x5
x3
=
x3-5
=
x-2
1
Since the exponent is negative
When dividing variables with exponents
the x moves to the denominator
and the exponent becomes positive
subtract the exponents
x5
x3
=
x3-5
=
x-2
1
=
x2
1
x8
x2
=
x
9xy2
6x6y4
=
x
y
Negative exponents always go
Negative exponents always go
the opposite place 
Negative exponents always go
so if the negative exponent is in the numerator
the opposite place 
Negative exponents always go
so if the negative exponent is in the numerator
the opposite place 
x-3
1
Negative exponents always go
so if the negative exponent is in the numerator
it moves down and becomes positive
the opposite place 
x-3
1
Negative exponents always go
so if the negative exponent is in the numerator
it moves down and becomes positive
the opposite place 
x-3
1
=
1
x3
Negative exponents always go
so if the negative exponent is in the numerator
but if the negative is in the denominator
it moves down and becomes positive
the opposite place 
x-3
1
=
1
x3
Negative exponents always go
so if the negative exponent is in the numerator
but if the negative is in the denominator
it moves down and becomes positive
the opposite place 
x-3
x-3
1
1
=
1
x3
Negative exponents always go
so if the negative exponent is in the numerator
but if the negative is in the denominator
it moves down and becomes positive
the opposite place 
x-3
x-3
1
1
=
=
1
x3
Negative exponents always go
so if the negative exponent is in the numerator
but if the negative is in the denominator
it moves down and becomes positive
the opposite place 
x-3
x-3
1
1
=
=
x3
1
1
x3
Negative exponents always go
so if the negative exponent is in the numerator
but if the negative is in the denominator
it moves down and becomes positive
the opposite place 
x-3
x-3
1
1
=
=
x3
1
1
x3
it moves to the numerator
Which of these variables move?
 x, y, z
x, b, c
a, b, c
a, y, z
x-2yz2
ab-1c-2
When taking a power to a power
When taking a power to a power
(x2)3
When taking a power to a power
the exponents are multiplied
(x2)3
When taking a power to a power
the exponents are multiplied
(x2)3
=
When taking a power to a power
the exponents are multiplied
(x2)3
=
x2•3
When taking a power to a power
the exponents are multiplied
(x2)3
=
x2•3
= x6
(x4)3 =
x
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