Transcript Exponents

Exponents
Location of Exponent
 An
exponent is a little number high
and to the right of a regular or base
number.
Base
3
4
Exponent
Definition of Exponent
 An
exponent tells how many times
a number is multiplied by itself.
Base
3
4
Exponent
What an Exponent Represents
 An
exponent tells how many times
a number is multiplied by itself.
4
3 =3x3x3x3
How to read an Exponent
 This
exponent is read three to the
fourth power.
Base
3
4
Exponent
How to read an Exponent
 This
exponent is read three to the
2nd power or three squared.
Base
3
2
Exponent
How to read an Exponent
 This
exponent is read three to the
3rd power or three cubed.
Base
3
3
Exponent
Read These Exponents
2
3
5
3 2 6 7
4
What is the Exponent?
2x2x2= 2
3
Any number to the 1st power
equals that number.
6¹ = 6
Any number to the zero power
equals one.
8º = 1
4º = 1
2005º = 1
What is the Exponent?
3x3= 3
2
What is the Exponent?
5x5x5x5= 5
4
What is the Base and the
Exponent?
8x8x8x8= 8
4
What is the Base and the
Exponent?
7 x 7 x 7 x 7 x 7 =7
5
What is the Base and the
Exponent?
9x9= 9
2
How to Multiply Out an
Exponent to Find the
Standard Form
4
3 =3x3x3x3
9
27
81
What is the Base and Exponent
in Standard Form?
4
2
= 16
What is the Base and Exponent
in Standard Form?
2
3
= 8
What is the Base and Exponent
in Standard Form?
3
1
= 3
What is the Base and Exponent
in Standard Form?
5
0
= 1
Exponents Are Often Used in
Area Problems to Show the
Feet Are Squared
Length x width = area 15ft.
A pool is a rectangle
30ft
Length = 30 ft.
Width = 15 ft.
2
Area = 30 x 15 = 450 ft.
Exponents Are Often Used in
Volume Problems to Show the
Centimeters Are Cubed
Length x width x height = volume
A box is a rectangle
Length = 10 cm.
20
10
Width = 10 cm.
10
Height = 20 cm.
Volume =
3
20 x 10 x 10 = 2,000 cm.
Here Are Some Areas
Change Them to Exponents
40 feet squared = 40 ft. 2
2
56 sq. inches = 56 in.
2
38 m. squared = 38 m.
2
56 sq. cm. = 56 cm.
Here Are Some Volumes
Change Them to Exponents
3
30 feet cubed = 30 ft.
3
26 cu. inches = 26 in.
44 m. cubed = 44 m.3
3
56 cu. cm. = 56 cm.
Exponents of Ten
Notice that the number of zeros
matches the exponent number
2
10
3
10
4
10
5
10
100
1,000
10,000
100,000
Exponents of Ten
What Is the Standard Form
of These Tens?
2
10
3
10
4
10
5
10
100
1,000
10,000
100,000
Multiplying Multiples of Ten
Multiply These Numbers
100 x 2 =
200
1,000 x 3 =
3,000
10,000 x 7 = 70,000
100,000 x 9 = 900,000
Multiplying Multiples of Ten
Did you notice that all you
have to do is multiply 1 x whole
number & add the zeros behind?
100 x 2 =
200
1,000 x 3 =
3,000
10,000 x 7 = 70,000
100,000 x 9 = 900,000
Short Cut for Writing Large
Numbers
Combine these two steps for
writing large numbers.
2
6 x 10 = 600
6 x (10 x 10) = 6 x 100 = 600
Short Cut for Writing Large
Numbers
Remember!
The exponent is the same as the
number of zeros.
2
6 x 10 = 600
What is the Standard Number?
2
7 x 10 = 700
What is the Standard Number?
3
8 x 10 = 8,000
What is the Standard Number?
4
9 x 10 = 90,000
What is the Standard Number?
2
4 x 10 = 400
What is the Exponent Form?
700,000 = 7 x 10
5
What is the Exponent Form?
500 = 5 x 10
2
What is the Exponent Form?
3
6,000 = 6 x 10
What is the Exponent Form?
4
90,000 = 9 x 10