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Copyright © Lynda Greene Aguirre 2009
1
Exponential Form is used when you want to
multiply the same number by itself several times.
The “base” is
the actual
number we will
multiply
5
4
The “power” is
how many bases
will be
multiplied.
Read as: Five to the Fourth power
5 is the base
4 is the power (also called the exponent)
Copyright © Lynda Greene Aguirre 2009
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Definitions:
5 x 5 x 5 x 5 is called EXPANDED NOTATION
5
4
is called EXPONENTIAL NOTATION
Copyright © Lynda Greene Aguirre 2009
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For example:
5
4
five to the fourth power
means to perform this multiplication:
5 x 5 x 5 x 5, (multiply four 5’s together).
5 x 5 x 5 x 5 = 625
Answer
Copyright © Lynda Greene Aguirre 2009
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Using a Calculator to evaluate exponents
Calculators use different buttons, but the most common one
is this one ^ .
4
A problem like
3
(four to the third power)
Means 4 x 4 x 4 = 64
Enter it in the calculator as: 4 ^ 3 = 64
Copyright © Lynda Greene Aguirre 2009
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Using your calculator, evaluate the following exponents:
12 
22 
32 
42 
52 
62 
72 
82 
9 
10 2 
11 
12 
132 
14 2 
15 2 
2
Copyright © Lynda Greene Aguirre 2009
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2
6
Exponent Expansion
Write in Expanded Form, then evaluate (if possible)
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Exponent Rules
Rule:
8
Exponent Rules: double powers
Notice that you can get the same answer by multiplying the powers
Rule:
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Exponent Rules
Expand and evaluate each problem below
You can cancel the same number (top and
bottom)as long as it’s multiplication
Need to put a “1” on the bottom if
all the numbers are wiped out in the
cancelling step
Need to put a “1” on top if all the
numbers are wiped out in the
cancelling step
Notice that you can get to the same answer by subtracting the powers
(top-bottom)
Rule:
10
Copyright © Lynda Greene Aguirre 2009
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The Exponent, or power, indicates how many bases
should be multiplied. When the power is a zero, that
means that there are no bases.
The “power”
indicates that
there will be no
3’s
0
3
Copyright © Lynda Greene Aguirre 2009
Read as: Three to the zero’th power
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However, this is not equal to zero, it is defined as:
3 1
0
Definition of a Zero Exponent:
Anything raised to the zero’th power is equal to “1”
It doesn’t matter what is
being raised the power of
zero, it will be equal to the
number “1”.
Copyright © Lynda Greene Aguirre 2009
x 1
0
(5 x) 0  1
( x  3 y  6) 0  1
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Copyright © Lynda Greene Aguirre 2009
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Negative Exponents
First write the base as a fraction
(if it’s not already written that way)
Move the 4’s to the bottom
and tear up the parking ticket
Parking Ticket: The
negative power means that
the base (the “4” in this
case) is in the wrong place.
Since this is a fraction,
there are only two
“parking places”,
the top
or the bottom.
(i.e. change the negative power
into a positive power)
Finish the problem
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Practice Problems
 7x  
5x 2 
2
 
3
3 0
2
 42 x  
0

63 
81 x 2 
Copyright © Lynda Greene Aguirre 2009
4
50
2

4 x 3

1 2
2 y
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