Download 8.2 ppt

8.2- Zero and Negative
Exponents
Bell Work:
 Evaluate each expression:
 1. 42
 2. (-2)3
 3. (1/2)3
 4. 2 * 1.053
 5. 34 * 33
Answers:
 1. 16
 2. -8
 3. 1/8
 4. 2.205
 5. 2187
8.2 Zero and Negative
Exponents
I can evaluate powers that
have zero and negative
exponents.
Zero and Negative
Exponents
Let ‘n’ be a positive integer and ‘a’ be a nonzero
number.
Negative Exponents
a
n
1
 n
a
reciprocals
2
3 
1 1

2
3
9
Zero Exponents
a 1
0
5  1
0
A nonzero number to the zero
power has the value of ONE. ANY
NUMBER (except zero!) RAISED TO
THE ZERO POWER IS ONE!!!!
Example
What this really means is that you turn a negative exponent
into a positive exponent by shifting the power from
numerator to denominator or vice versa!
1 1
2  2 
2
4
2
1
1
4  3
4
64
3
Important – only move the base number and the negative exponent
that goes with it!
Evaluate the expressions.
1)
3)
4
3
1
 
3
1
1

3
4
64
2

1
1
 
3
1

1
 
9
9
2
2)
0
4)
9
0
1
 9
0
(5)  1
Simplify expressions: write with positive
exponents.
(-5)-3 =
1
= -1
(-5)3
125
244-3 = 24 ∙ 1 = 24∙ 1 = 3
43
-3-4 = 1 = - 1
4
-3
81
64
8
Simplify expressions: write with positive
exponents.
3a-3b-2 = 33 2
ab
(3-3)2=
3(-3 ∙ 2)
=
3-6 =
1
1
=
6
3
729
Graphing with a variable
as an exponent
Sketch the graph of y = 2x
x
2
1
2x
4
2
0
-1
20=1 2-1= ½
-2
2-2 = ¼
Example: (Just follow this example to see what you
get to do on your assignment.)
Between 1970 and 1990, the Missouri
population increased at a rate of .47%
per year. The population P in t years is
given by:
P = 4,903,000 1.0047t
Where t = 0 for 1980
Find the population in 1970, 1980, and 1990
To find the population, plug the numbers into
the formula and then use a calculator.
Pop in 1970 t = -10
Pop in 1990 t = 10
Do you expect it to be more
or less in 1970 than 1980?
P = 4,903,000  1.0047-10 (set up the problem)
= 4,678,406
(calculate)
This is the population in 1970.
Population in 1990:
P = 4,903,000  1.004710
P = 5,138,376
Assignment
8.2 (pg. 459- 460)
#14-50, #64 EVEN