RATIONAL EXPONENTS Basic terminology Substitution and evaluating Laws of Exponents Multiplication...
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Transcript of RATIONAL EXPONENTS Basic terminology Substitution and evaluating Laws of Exponents Multiplication...
Basic Terminology
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,
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,
TIONMULTIPLICA
repeatedundergoesthatVariableornumberthenotationlExponentiaInBase
factoraasusedis
basethetimesofnumberthenotationlExponentiaInExponent
42BASE
EXPONENTmeans 162222
Important Examples
IMPORTANT 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
Substitution and EvaluatingSTEPS
1.Write out the original problem.2.Show the substitution with parentheses.3.Work out the problem.
3;4: xxifSolveExample 3;4 xxifSolve
3)4( = 64
More Examples
Evaluate the variable expression when x = 1, y = 2, and w = -3
22 )()( yx
22 )()( yx
22 )2()1(
541
Step 1
Step 2
Step 3
2)( yx
2)( yx
2)2()1(
9)3( 2
Step 1
Step 2
Step 3
ywx
ywx
2)1)(3(
Step 1
Step 2
Step 3
3)1)(3(
MULTIPLICATION PROPERTIESPRODUCT OF POWERS
This 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 PROPERTIESPOWER TO A POWER
This 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 PROPERTIESPOWER OF PRODUCT
This 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
MULTIPLICATION PROPERTIESSUMMARY
PRODUCT OF POWERSbaba xxx
POWER TO A POWER baba xx
POWER OF PRODUCTaaa yxxy )(
ADD THE EXPONENTS
MULTIPLY THE EXPONENTS
ZERO AND NEGATIVE EXPONENTSANYTHING TO THE ZERO POWER IS 1.
27
1
3
13
9
1
3
13
3
1
3
13
13
33
93
273
33
22
11
0
1
2
3
22222
222
4
1
2
1
)2(
1)2(
2122
xxxx
xxx
8131
31
3
11
311
3
1 44
4
4
4
DIVISION PROPERTIES QUOTIENT OF POWERS
This property is used when dividing two or more exponential expressions with the same base.
))()((
))()()()((3
5
xxx
xxxxx
x
x 2
1
))((x
xx
7434
34
3
4
3 11111
xxxx
xxx
x
x
DIVISION PROPERTIESPOWER OF A QUOTIENT
12
8
43
424
3
2
)(
)(
y
x
y
x
y
x
Hard Example
3
43
2
3
2
yx
xy
343
32
)3(
)2(
yx
xy
1293
633
3
2
yx
yx
69
123
27
8
yx
yx
69
123
27
8
yx
yx6
6
27
8
x
ySummary of Zero, Negative, and Division Properties