Exp2 Negative Exponents
What would  10-2  equal?

Negative exponents  indicate a fraction or decimal

(a number between o and 1).  They are not negative

 by themselves.  For example 4-3 is the following.

  =  1

        100

 =  100
4 x 4 x 4
1

  =   1

          20

 =   1

         10

 
=
64
1
What would  2-3  equal?

Negative exponents  indicate a fraction or decimal (a

number between o and 1).  They are not negative by

themselves.  For example 4-3 is the following.

=     1

           6

 =    8

 
4 x 4 x 4

  =    ¼

 =     ⅛

1
=
64
1
What would  3-2  equal?

Negative exponents  indicate a fraction or decimal (a

number between o and 1).  They are not negative by

themselves.  For example 4-3 is the following.

 =     9

 =   -9

 
4 x 4 x 4
1

 =    1

           6

=   1

         9

=
64
1
What would  -3-2  equal?

A negative sign in front of the exponent will reverse

 the direction of the answer.  For example -4-3 is as

follows:

=     9

 =    -9

 
-
4 x 4 x 4
1

 =   1

          9

=  -

=
-

1

9

64
1
What would  -3-3  equal?

A negative sign in front of the exponent will reverse

 the direction of the answer.  For example -4-3

is as follows:

 

 

 =   27

=  - 27

-
4 x 4 x 4
1
 =    1
= -
=

  27

  1

 27

-
64
1
What would  -2-3  equal?

A negative sign in front of the exponent will reverse

the direction of the answer.  For example -4-3 is as

follows:

 =  ⅛
 =  -⅛
-
4 x 4 x 4
1
 =   8
=  -8
=
-
64
1
What would  (-2)-3  equal?

A set of parenthesis around the number like below

makes every number being multiplied negative. 

The answer can be positive or negative depending on

odd or even amount of negative signs.

 

 

= -

= ⅛

(-4)-3 =

1
6
-4 x -4 x -4
1
= -⅛

= -

=
-

 6

1
64
1
= −
What would  (-2)-4  equal?
= −

A set of parenthesis around the number like below

makes every number being multiplied negative.  The

answer can be positive or negative depending on odd

or even amount of negative signs.

16

(-4)-3 =

8

1
1
-4 x -4 x -4
1

=

=

=

 16

  8

 
-
1
1
64
1
What would  70  equal?

x0  equals 1 and x1  equals x.

   = 1
 =

  7

1
 =    0
 =
-

  7

 
1
What would  71  equal?

x0  equals 1 and x1  equals x.

 =  7

 
 = 1
  =   0
 =

  7

 
1
What would  7-1  equal?

 =  7

 
 =  1

x0  equals 1 and x1  equals x.

  =   0
 =

  7

 
1
What would  10000  equal?

  = 100

 
  =   1

x0  equals 1 and x1  equals x.

 =   1000
 =

1000

 
1
What would  2x-4  equal?
 =

A number in front of the one in exponent form with

no sign between them is being multiplied by the

exponent.  If the exponent is a fraction, the number in

front goes over one to multiply it by the exponent. 

See the example below.

3x-3  =

2x4

 =

3

1

x

2x4

1

x3

1
=
 =
x3
3
x4
2
What would  3x-3  equal?
 =

A number in front of the one in exponent form with no

sign between them is being multiplied by the

exponent.  If the exponent is a fraction, the number in

front goes over one to multiply it by the exponent. 

See the example below.

3x-3  =

3x3

 =

3

1

3x3

x

1
1

x3

 =
=
x3

3

x3
3
What would  -4x-3  equal?
 =

A number in front of the one in exponent form with no

sign between them is being multiplied by the

exponent.  If the exponent is a fraction, the number in

front goes over one to multiply it by the exponent. 

See the example below.

3x-3  =

-4x3

 =

3

1

-4x3

1

x

x3

1
 =
=

-4

x3
x3
3
What would  42  x 44   equal?
 =

42  x 43    =

Since 42  is 4 x 4 and 43  is 4 x 4 x 4 and 4 x 4 x 4 x

4 x 4 is 45  , 42  x 43  equals the following:

46

4 x 4 x 4 x 4 x 4 = 4(2 + 3)

 =

48

 =

46

1

=
45
What would  42  x  4-4   equal?
 =

42  x 43    =

Since 42  is 4 x 4 and 43  is 4 x 4 x 4 and 4 x 4 x 4 x 4

 x 4 is 45  , 42  x 43  equals the following:

46

4 x 4 x 4 x 4 x 4 = 4(2 + 3)

 =

4-8

 =

42

1

=
45
What would  42  x  4   equal?
 =

42  x 43    =

Since 42  is 4 x 4 and 43  is 4 x 4 x 4 and 4 x 4 x 4

x 4 x 4 is 45  , 42  x 43  equals the following:

43

4 x 4 x 4 x 4 x 4 = 4(2 + 3)

 =

42

 =

42

1

=
45
What would  44  ÷  42   equal?
 =

43  ÷ 42    =

Since we add on multiplication exponent patterns, we

 need to subtract on division ones.

43

 =
4 x 4 x 4
4 x 4

42

=
 =

 4(3 - 2)

42

1

=
41
What would  45  ÷  42   equal?
 =

43  ÷ 42    =

Since we add on multiplication exponent patterns, we

need to subtract on division ones.

43

 =
4 x 4 x 4
4 x 4

42

=
 =

 4(3 - 2)

42

1

=
41
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