8.2 Apply Exponent Properties Involving Quotients

!PPLY %XPONENT 0ROPERTIES
)NVOLVING 1UOTIENTS
+ 5SE PROPERTIES OF EXPONENTS INVOLVING QUOTIENTS
'OAL
9OUR .OTES
15/4)%.4 /& 0/7%23 02/0%249
,ET A BE A NONZERO REAL NUMBER AND LET M AND N BE
POSITIVE INTEGERS SUCH THAT M N
7ORDS 4O DIVIDE POWERS HAVING THE SAME BASE
Ê ÃÕLÌÀ>VÌÊ THE EXPONENTS
M
A
Ê “ÊÊ˜Ê A p !LGEBRA ]
N z A
A
%XAMPLE ]z Ê ÇÊÊÓÊ Ê xÊ
%XAMPLE 5SE THE QUOTIENT OF POWERS PROPERTY
3IMPLIFY THE EXPRESSION
A ]
z Ê £ÓÊÊxÊ Ê ÇÊ
7HEN SIMPLIFYING
POWERS WITH
NUMERICAL BASES
ONLY WRITE YOUR
ANSWERS USING
EXPONENTS
B ] z Ê ÇÊÊ{Ê Ê ÎÊ
+ Ê £äÊ
]Ê
z
z
C ]
Ê £äÊÊ{
Ê { ÈÊ
Y z
D ]z+ Y ]
Y
Y
z
z
zY Ê £ÓÊʙ
z
z
zÊ Þ ÎÊ
,ESSON s !LGEBRA .OTETAKING 'UIDE
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
9OUR .OTES
0/7%2 /& ! 15/4)%.4 02/0%249
,ET A AND B BE REAL NUMBERS WITH B p AND LET M BE
A POSITIVE INTEGER
7ORDS 4O FIND A POWER OF A QUOTIENT FIND THE POWER OF
THE Ê ˜Õ“iÀ>̜ÀÊ AND THE POWER OF THE Ê `i˜œ“ˆ˜>̜ÀÊ
AND DIVIDE
A M
7HEN SIMPLIFYING
POWERS WITH
NUMERICAL AND
VARIABLE BASES
EVALUATE THE
NUMERICAL POWER
>“
{Î
]Êz
%XAMPLE |]
z
????
ÇÎ
!LGEBRA |]
z
B
]
ÊÊz B p L“
????
%XAMPLE 5SE THE POWER OF A QUOTIENT PROPERTY
3IMPLIFY THE EXPRESSION
R
Àx
A |]z Ê ]
Ê
Êz
S
Ãx
????
­{®Î
È{
z |]ÊÊÊz Ê Ê]
ÊÊ
z
Ê z]
Ê ÎÊÊÊ
z
Ê z Ê]
Ê ÎÊÊz
B |]
W
Ü
Ü
Ü
ÜÎ
????
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??????
??????
{ È{
#HECKPOINT 3IMPLIFY THE EXPRESSION
] z
+ ]
z
­n®ÎÊ
Ê ÎÈ
R |]T z
|]
z
ÀÓ
™
]ÊÊÊz
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Ê ]
ÊÈÓx
ÊÊ
zÊ
{
Ì
,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
5SE PROPERTIES OF EXPONENTS
%XAMPLE Y Y 3IMPLIFY |]
z 3OLUTION
Y Y ­ÓÞ Ç®Î
­Þ x®Î
|]
z Ê Ê]ÊÊÊ
z
Ê
Ê
Ê *œÜiÀʜvÊ>ʵ՜̈i˜ÌÊ PROPERTY
ÓÎÊ+Ê­Þ Ç®Î
zÊ Ê]
Ê Ê
ÊzÊ Ê ÊÊ*œÜiÀʜvÊ>Ê«Àœ`ÕVÌÊÊÊ PROPERTY
xÎ
Ê Ê
Ê
­Þ ®
nÞ Ó£
z
Ê
zÊ ]
Ê £xÊÊÊ
Ê ÊÊÊÊÊ*œÜiÀʜvÊ>Ê«œÜiÀÊÊÊÊÊ PROPERTY
Ê
Ê nÞ ÈÊ
Ê Ê+՜̈i˜ÌʜvÊ«œÜiÀÃÊÊ PROPERTY
Þ
#HECKPOINT 3IMPLIFY THE EXPRESSION
Y Z Y
|]z
{™Þ xâ ÓÊ
M N |]
z
MN
n“ȘÎÊ
S
T S
]
z + |]z
T
Ê £ÈÃÌ Ó
AB ]
z+ |]
A z
B
A
Ê È{>xL£ä
(OMEWORK
,ESSON s !LGEBRA .OTETAKING 'UIDE
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