8.3 Define and Use Zero and Negative Exponents

$EFINE AND 5SE :ERO AND
.EGATIVE %XPONENTS
'OAL
9OUR .OTES
+ 5SE ZERO AND NEGATIVE EXPONENTS
$%&).)4)/. /& :%2/ !.$ .%'!4)6% %80/.%.43
7ORDS
!LGEBRA
%XAMPLE
A TO THE ZERO POWER
IS A Ê £Ê A p Ê £Ê
AN IS THE RECIPROCAL
OF AN
£
AN Ê Ê]
ÊÊz A p >˜
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£
Ê Ê]
Êz
Ó
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AN IS THE RECIPROCAL
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ʘÊz A p >
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£
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Ê Êz
Ó£
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%XAMPLE 5SE DEFINITION OF ZERO AND NEGATIVE EXPONENTS
%VALUATE THE EXPRESSION
Ê£ÎÊÊz
A Ê ]
Ó
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Ê
$EFINITION OF Ê ˜i}>̈ÛiÊ
iÝ«œ˜i˜ÌÃÊ
£
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n
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Ê
%VALUATE EXPONENT
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Ê
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$EFINITION OF Ê âiÀœÊiÝ«œ˜i˜ÌÊ
Ê
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iÝ«œ˜i˜ÌÃÊ
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%VALUATE EXPONENT
Ê È{Ê ÊÊ
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£
È{
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Ê ÊÊz
]
D Ê Õ˜`ivˆ˜i`Ê
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AN IS DEFINED ONLY FOR
A Ê ˜œ˜âiÀœÊ NUMBER A
,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
02/0%24)%3 /& %80/.%.43
,ET A AND B BE REAL NUMBERS AND LET M AND N BE
INTEGERS
AM + AN A Ê “ÊʘÊ
Ê ÊÊÊÊ*Àœ`ÕVÌʜvÊ«œÜiÀÃÊÊÊÊ PROPERTY
­AM®N A Ê “˜Ê
Ê ÊÊÊÊÊ*œÜiÀʜvÊ>Ê«œÜiÀÊÊÊÊÊ PROPERTY
ABM Ê >“L“Ê
Ê Ê*œÜiÀʜvÊ>Ê«Àœ`ÕVÌÊÊ PROPERTY
AM
A
“
A M
Ê>“ÊÊz B p ]
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L
Ê “ÊÊ˜Ê A p ]
N z A
%XAMPLE Ê Ê+՜̈i˜ÌʜvÊ«œÜiÀÃÊÊ PROPERTY
Ê *œÜiÀʜvÊ>ʵ՜̈i˜ÌÊ PROPERTY
%VALUATE EXPONENTIAL EXPRESSIONS
%VALUATE THE EXPRESSION
A + Ê ­x®{ÊÊ­{®Ê
Ê xäÊ
Ê ``Ê EXPONENTS
Ê £Ê
$EFINITION OF
Ê âiÀœÊiÝ«œ˜i˜ÌÊ
B ­®Ó Ê xÓÊ+Ê­Ó®Ê
Ê ÕÌˆ«ÞÊ
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Ê ÈÓxÊ
%VALUATE POWER
Ê £ÈÊ
D ]
z Ê ÎÓÊÊ­£®Ê
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Ê *œÜiÀʜvÊ>Ê
«œÜiÀÊ PROPERTY
Ê x{Ê
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z Ê {ÓÊ
0RODUCT OF POWERS
PROPERTY
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iÝ«œ˜i˜ÌÃÊ
%VALUATE POWER
Ê +՜̈i˜ÌʜvÊ
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Ê ÎÎ Ê
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EXPONENTS
Ê ÓÇÊ
%VALUATE POWER
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9OUR .OTES
#HECKPOINT %VALUATE THE EXPRESSION
]
z
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z
nÊ
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z
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%XAMPLE 5SE PROPERTIES OF EXPONENTS
W X
3IMPLIFY THE EXPRESSION ]z7RITE YOUR ANSWER USING
WX
ONLY POSITIVE EXPONENTS
3OLUTION
WX
WX
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Ü Î­ÓÜÝ®Ó
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Ê Êz
Ê ÊÊ
$EFINITION OF NEGATIVE EXPONENTS
ÓÝ
Ê Ê]
Ê
Êz
ÊÊ Ê Ê*œÜiÀʜvÊ>Ê«Àœ`ÕVÌÊÊ PROPERTY
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Ê ÊÊÊ*Àœ`ÕVÌʜvÊ«œÜiÀÃÊÊÊ PROPERTY
Ê ÊÊÊÊÊ ]
Ê £xÊ ÊzÊÊÊÊÊ ÊÊ
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Ê +՜̈i˜ÌʜvÊ«œÜiÀÃÊ PROPERTY
#HECKPOINT 3IMPLIFY THE EXPRESSION
FG
z
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Î
v} x
Ê ]
Ê £ÓÊ{Êz
F G
(OMEWORK
]Ê Êz
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™Þ â
,ESSON s !LGEBRA .OTETAKING 'UIDE