7/3/2015 11:50 amr.2 - integer exponents1 exponents section r.2
TRANSCRIPT
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Exponents
Section R.2
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Definitions
Base: The term/variable of which is being raised upon
Exponent: The term/variable is raised by a term. AKA Power
ma BASEBASE
EXPONENTEXPONENT
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Definitions
ma 322 2 2
2 3 2 2 2
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Definitions
no negative exponents!
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Example 1
3 3 9
9
2(3)
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Example 2
3 3 9
9
2( 3)
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Example 3
9
23
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Example 4
2
1
3
1
9
2(3)
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Example 5
3
23
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Warm-Up Solve:
3
3
3
3
1 41.
2 7
2. 2
3. -2
4. - 2
5. 2
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Properties of ExponentsNegative Power Property:
Product of a Power:
Power of a Power:
Power of a Product:
Quotient Power Property:
m n m na a a ( ) m n m na a
( ) m m mab a b
( ) 1nn
aa
m
m nn
aa
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n na bb a
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Negative Power Property
Saying goes: NO NEGATIVE POWERS
What are the base(s) and the power(s)?
3a
( ) 1nn
aa
n na bb a
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Negative Power Property
( ) 1nn
aa
( )aa
33
1
3( )a
Negative Power Property
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( ) 1nn
aa
n na bb a
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Product of a Power
Saying goes: BASE, BASE, ADD
If the BASES are same, ADD the powers
What are the base(s) and the power(s)?
4 52 2
m n m na a a
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Product of a Powerm n m na a a
4 5 4 52 2 2 92
512
4 52 2
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Product of a Powerm n m na a a
4 5 4 52 2 2 92
512
4 52 2
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Your Turn4 52 2
2
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Power of a Power
Saying goes: POWER, POWER, MULTIPLY
If the POWERS are near each other, MULTIPLY the powers – usually deals with PARENTHESES
What are the base(s) and the power(s)? 323
( ) m n m na a
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Power of a Power
( ) m n m na a
32 63 3
63
729
323
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Power of a Power
( ) m n m na a
232
64
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Your Turn
( ) 3 22
1
64
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Power of a Product
Saying goes: DISTRIBUTE THE POWER TO THE BASES
What are the base(s) and the power(s)?
( )43x
( ) m m mab a b
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Power of a Product
( ) m m mab a b
4 4 4(3 ) (3) ( )x x
481 x
x 481
4(3 )x How many
bases does this problem have?
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Power of a Product
( ) m m mab a b
y
x
3
3
x y1 3( )
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Your Turn
( ) m m mab a b
x 664
3 2( 8 )x
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Quotient Power Property
Saying goes: When dividing an expression with a power, SUBTRACT the powers. They must have the same base in order to subtract.
What are the base(s) and the power(s)?
8
3
x
x
m
m nn
aa
a
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Quotient Power Property
mm n
n
aa
a
8
8 33
xx
x
8
3
x
x 5x
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Quotient Power Property
mm n
n
aa
a
3
8
x
x
5
1
x
Your Turn
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=
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Assignment
Pg 27 73-93 odd