exponents

1. ALL ABOUT
EXPONENTS
Adam Brewster

2. Objective
 At the conclusion of this slide show you will be
able to the following:
 Write numbers in exponential form
 Evaluate expressions with exponents
 Evaluate expressions with negative exponents
 And evaluate the zero exponent

3. Vocabulary
 Base – the number that is being used as a factor.
 Exponent – tells you how many times the base is to be
multiplied.
 Exponential Form – when a number is written with a
base and an exponent.
 Power – the number that is produced by raising a base
to an exponent.
 Reciprocal – is 1 divided by the number itself

4. Writing exponents
 How do I write something in exponential form?
 4•4•4•4•4•4•4•4
 Identify how many times 4 is being used as a factor.
(In this case 4 is being used as a factor 8 times, so 8
would be our exponent.)
 Write in exponental form, 4 • 4 • 4 • 4 • 4 • 4 • 4 • 4
Would be written as

5. Now you try
 Write the following in exponential form
1. 3•3•3•3
2. x•x•x•x•x•x
3. 7•7•7•y•y•y•y
4. (- 4) • (- 4) • (- 4) • (- 4) • (- 4) • (- 4)

6. Answers
1. 3•3•3•3=
2. x•x•x•x•x•x=
3. 7•7•7•y•y•y•y= •
4. (- 4) • (- 4) • (- 4) • (- 4) • (- 4) • (- 4) =

7. How do I evaluate powers?
 Simply by multiplying your base by the number of
times indicated by the exponent.
 So you would find the product of 5 being
multiplied three times. 5 • 5 • 5 = 125
 Watch negative numbers means you are
multiplying -5 twice. So (-5) • (-5) = 25
 And means you are multiplying 5 twice and
making your answer negative
– (5 • 5 ) = -25

8. Now you try
1.
2.
3.
4.

9. Answers
1. = -64
2. = -16
3. =8
4. = 144

10. What’s up with negative exponents?
 Any negative exponent can be written as the
reciprocal of the base raised to the positive
exponent.
 What that means in plain English is that
can be written as , now to evaluate this
you would multiply • =

11. Now you try
1.
2.
3.

12. Answers
1. = =
2. = =
3. = =

13. Can zero be an exponent?
 YES it can! He is how zero works as an
exponent.
 Now this is very complicated…
 and you need to commit this to memory…

14. any number to the zero
power is … 1

15. Exponent zero continued
 That means if you have your answer will
be 1.
 Or even if you have you answer will
still be 1.

16. Now you try
1.
2.
3.

17. Answers
Your answers all should be 1.

18. Objective Check
 You should now be able to explain the following terms in
your own words :
 Base
 Exponent
 Exponential Form
 Power
 Reciprocal
 You should also be able to:
 Write numbers in exponential form
 Evaluate expressions with exponents
 Evaluate expressions with negative exponents
 And evaluate the zero exponent

19. References
 Holt, Rienhart, and Wilson. Holt Mathematics
Course 3. (2007)