Section 2.8 3.1 powers and exponents - squ root (math)
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Transcript of Section 2.8 3.1 powers and exponents - squ root (math)
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Sept. 09, 2010 Thursday’s Quiz:
Lesson 2-2 Comparing and Ordering Rational Numbers (compare fractions)
Lesson 2-8 Powers and ExponentsLesson 3-1 Square RootsLesson 3-2 Estimating Square RootsLesson 3-3 The Real Number System (compare
square roots)Lesson 4-1 Ratios and Rates
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Section 2.8POWERS and EXPONENTS
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Basic Terminology
.
,
.
,
TIONMULTIPLICA
repeatedundergoesthatVariableornumberthenotationlExponentiaInBase
factoraasusedis
basethetimesofnumberthenotationlExponentiaInExponent
42BASE
EXPONENTmeans 162222
Important Examples
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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
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Variable Expressions
))()((
))()()()(()(
3
5
yyymeansy
xxxxxtionmultiplicaforsparentheseusemeansx
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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
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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
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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
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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(
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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
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ZERO and NEGATIVE PROPERTIES
Zero power
1)( 0 x
Negative Exponents
aa
aa
xx
andx
x
1
1
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Section 3.1
Square Roots
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Find each square roots:
√25 -√81 √(4/9)
Solve the equations:
Y2 = 36 E2 = 144S2 = 9 / 25
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Classwork / Homework:
Page 100 # 14 – 40 even
Wednesday’s work:Page 118 # 14 – 42 even