3.1 integer exponents
DESCRIPTION
handoutsTRANSCRIPT
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Integer Exponents
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Learning Objective
Upo n compl etion, you shoul d be able to
Perform opera tions invol ving integer
exponents.
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INTEGER EXPONENTS
Shortcut for w riting repeated products
( n copies of a, provided n is a posi tive
integer, a is the base, n is the exponent)
...
n
na a a a a a
43 3 3 3 3 81
3
2 2 2 2 8
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Laws of Exponents
0
:
31,
4
Example
0 1, 0a a
0
3 54 1
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Laws of Exponents
3
3
:
1 1 15
5 5 5 5 125
Example
1
, 0, 0nn
a a na
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Laws of Exponents
1. p q p qa a a
5 3 5 3 8
:
2 2 2 2
Example
Let , 0 and , 0a b R p q Z
2 5 2 5 3
3 3 3 3 27
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Laws of Exponents
2. p
p q
q
aa
a
55 3 2
3
:
22 2 4
2
Example
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Laws of Exponents
3. p p pab a b
5 5 5 5
:
2 2 32
Example
c c c
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Laws of Exponents
4.
p p
p
a a
b b
5 5
5
:
2 2 32
3 3 243
Example
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Laws of Exponents
5. qp pqa a
4 43 4 3 3 4 12
:
2 2 16 16
Example
s s s s
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Perform the indicated operation
and simplify.
2 31. 3 2 9 8 17
222. -3 2 9 4 5
22 2 2 2 43. 2 3 2 3 18x x x x x
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3
4 2 104. st s t
Perform the indicated operation
and simplify.
22 3 5
4 1 2
25.
3
a b c
a b c
22 4 3
12 3 0
256.
9
x y z
x y z
1
1 27. 2 3
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SUMMARY
p q p qa a a p
p qq
aa
a
( ) p p pab a b
( )p
pp
a a
b b
( )p q pqa a1nn
aa
0 1a
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Time to practice! -
Simplify the following:
1 31
2
0 2
30 2 2
1 25 1
4 21. 3.
9 4
2. 4.
sm n
r s
xyz x yb f
b x y z