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8.2 Negative and Zero
Exponents
I love exponents!
Definition of Negative Exponents
(let a be a nonzero number and let n be a positive integer)
The expression a-n is the reciprocal of
an .
n
1
=
a
a-n = 1
a≠0
a-n
an
3-2 = 1
32
=1
9
The negative exponent says the number
needs to be moved to the opposite location
and made positive.
If it’s negative in the numerator, it
belongs in the denominator position
positive.
If it’s negative in the denominator
position, it belongs in the numerator
position positive.
Definition of Zero Exponent
(let a be a nonzero number and let n be a positive integer)
A nonzero number to the zero power is
ALWAYS 1!
a0 = 1
a
0
30 = 1
(x2y5)0 = 1
The expression 00 is undefined.
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
3 2
1
0
-1
-2
-3
2x
8 4
2 20=1 2-1= ½ 2-2 = ¼ 2-3 = 1/8
Will it ever touch the x-axis?
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