exponents review
DESCRIPTION
TRANSCRIPT
EXPONENT LAWSEXPONENT LAWS
Basic TermsBasic Terms
.,
.,
TIONMULTIPLICArepeatedundergoesthatVariableornumberthenotationlExponentiaInBase
factoraasusedisbasethetimesofnumberthenotationlExponentiaInExponent
42BASE
EXPONENTmeans 162222
Important Examples
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
Variable ExpressionsVariable Expressions
))()((
))()()()(()(
3
5
yyymeansy
xxxxxtionmultiplicaforsparentheseusemeansx
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
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
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
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
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
DIVISION PROPERTIESDIVISION PROPERTIESPOWER OF A QUOTIENT
12
8
43
424
3
2
)()(
yx
yx
yx