exponents review
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EXPONENT LAWSEXPONENT LAWS
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Basic TermsBasic Terms
.,
.,
TIONMULTIPLICArepeatedundergoesthatVariableornumberthenotationlExponentiaInBase
factoraasusedisbasethetimesofnumberthenotationlExponentiaInExponent
42BASE
EXPONENTmeans 162222
Important Examples
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IMPORTANT EXAMPLESIMPORTANT EXAMPLES81)3333(34 means
81)3()3()3()3()3( 4 means
27)333(33 means
27)3()3()3()3( 3 means
Variable Examples
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Variable ExpressionsVariable Expressions
))()((
))()()()(()(
3
5
yyymeansy
xxxxxtionmultiplicaforsparentheseusemeansx
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MULTIPLICATION MULTIPLICATION PROPERTIESPROPERTIES
PRODUCT OF POWERSThis property is used to combine 2 or more exponential expressions with the SAME base.
53 22 )222( )22222( 82 256
))(( 43 xx ))()(( xxx ))()()(( xxxx 7x
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MULTIPLICATION MULTIPLICATION PROPERTIESPROPERTIES
POWER TO A POWERThis property is used to write and exponential expression as a single power of the base.
32 )5( )5)(5)(5( 222 65
42 )(x ))()()(( 2222 xxxx 8x
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MULTIPLICATION MULTIPLICATION PROPERTIESPROPERTIES
POWER OF PRODUCTThis property combines the first 2 multiplication properties to simplify exponential expressions.
2)56( )5()6( 22 9002536
3)5( xy ))()(5( 333 yx33125 yx
532 )4( xx 5323 ))(4( xx 5222 ))()(()64( xxxx
56 ))(64( xx 1164x
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ZERO AND NEGATIVE ZERO AND NEGATIVE EXPONENTSEXPONENTS
ANYTHING TO THE ZERO POWER IS 1.
271
313
91
313
31
313
13
33
93
273
33
22
11
0
1
2
3
22222
222
41
21
)2(1)2(
2122
xxxx
xxx
813131
311
311
31 4
4
4
4
4
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DIVISION PROPERTIES DIVISION PROPERTIES QUOTIENT OF POWERS
This property is used when dividing two or more exponential expressions with the same base.
))()(())()()()((
3
5
xxxxxxxx
xx
2
1))(( xxx
7434
34
3
4
3 11111
xxxx
xxx
xx
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DIVISION PROPERTIESDIVISION PROPERTIESPOWER OF A QUOTIENT
12
8
43
424
3
2
)()(
yx
yx
yx