10/29/2007
Exponentials and Logarithms Review
Math 148
The Laws (or Rules) of Exponents
1.
m
n
m
n
a
a
a
!
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#
2.
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%
m
n
m
n
a
a
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3.
1
0
"
a
4.
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a
a
1
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&
5.
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n
m
n
a
a
a
&
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6.
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n
m
m
n
m
n
a
a
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7.
(
)
k
k
k
a b
a
b
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8.
’
"
m
n
a
a
n = m
Comments
1.
This rule is true for all positive numbers
a
. This just states that when you multiply the
powers with the same base, the only thing you need to do to find the answer is to add
the exponents. It also implies that you should not change anything in the base.
2.
This is slightly different from what we have in 1. When we have a power of another
power, we multiply the exponents.
3.
This is a very important fact!
4.
Negative exponents should not be taken to mean negative numbers. They just indicate
repeated division!
6.
Calculations of higher degree roots and exponents have much in common.
7.
When we have a product and we raise that product to a single power
k
, each factor
must be raised separately to the one single power. This is true even when the bases
a
and
b
are different.
8.
This is true if
a
follows all the restrictions, including
1
(
a
.
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 Fall '08
 Mcginnis
 Exponents, Natural logarithm, Logarithm, false make true., make true. a.

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