1. Exponents

3. 4
Exponent 3
Base
Base - the repeated factor; the Big, Bottom number; the only number you may write as a factor.
tells you how many times to use the base as a repeated factor.
Exponent-

4. What an Exponent Represents4 3
= 3 x 3 x 3 x 3
exponential
form
product of
repeated (equal) factors
(expanded form)

5. three to the fourth power
How to read an Exponent 4 3
three to the fourth power

6. three to the 3rd power or three cubed2
three to the 2nd power
or three squared 3 3
three to the 3rd power or three cubed

7. 2 6 7 8 2 5 3 4 eight squared two cubed six to the fifth power
Read These Exponents 2 2 6 5 7 8 3 4
eight
squared
two
cubed
six to
the fifth
power
seven to
the fourth
power

8. What is the Exponent?
2 x 2 x 2 = 3 2 2
3 x 3 = 3 4
5 x 5 x 5 x 5 = 5

9. What is the Base and the Exponent?4
8·8·8·8 = 8
7·7·7·7·7 = 7 5 9 2
9·9 =

10. How to evaluate an exponent by multiplying out.4 3
= 3 x 3 x 3 x 3 9 27 81

11. 2 16 4 =
Evaluate: 3 2 9 = 4 16 2 = 3
125 5 =

12. 1 raised to any power will always be 1.
A Few to Memorize!!!
1 raised to any power will always be 1. 3 1
1 =
1 = 1 15
1,309 = 1

13. 5 = 1 1 8 = 1 23 = Any number raised to the
power of zero will always be one.
5 = 1 1
8 = 1
23 =

14. 16 8 4 2 1 Proof: 2 = 2³ = 2² = 2¹ = 2° = See a pattern?
How does that work?
Proof: 2 = 2³ = 2² = 2¹ = 2° = 16 8 4
See a pattern? 2 1

15. 5 = 5 15 = 15 8 = 8 Any number raised to the
power of one will always be itself.
5 = 1 5 1
15 = 15 1
8 = 8

16. Base 10
An exponential expression with a base of ten can be evaluated by writing the number 1 followed by a number of zeros that match the exponent. 2
= 100 10 5
= 100,000 10

17. area = length x width A pool is a rectangle Length = 30 ft.
Exponents Are Often Used in Area Problems to Show the units Are Squared
area = length x width
A pool is a rectangle
Length = 30 ft.
Width = 15 ft.
A = 30ft x 15ft = 450 ft
15ft.
30ft 2

18. Volume = length x width x height A box is a rectangle Length = 10 cm
Exponents Are Often Used in Volume Problems to Show the units Are Cubed
Volume = length x width x height
A box is a rectangle
Length = 10 cm
Width = 10 cm
Height = 20 cm
Volume =
10cm x 10cm x 20cm = 2,000 cm 20 10 10 3

19. Here Are Some Areas Change Them to Exponents2
40 feet squared = 40 ft
56 sq. inches = 56 in
38 m squared = 38 m
56 sq. cm = 56 cm 2 2 2

20. Here Are Some Volumes Change Them to Exponents3
30 feet cubed = 30 ft
26 cu. inches = 26 in
44 m cubed = 44 m
56 cu. cm = 56 cm 3 3 3