it - muse technologiesdblair.weebly.com/uploads/4/3/6/0/4360737/98-112_exponents.pdfstep 1: review...

$: It - Muse TECHNOLOGIESdblair.weebly.com/uploads/4/3/6/0/4360737/98-112_exponents.pdfStep 1: Review fractional exponents. The denominator of a fractional exponent tells you what root$
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X 4 2y

TlOWT

Write as a power

(006) (006) (006) (006)

Step 1 Identify the term that is multiplied repeatedly

The term (006) is repeated several times in the expression This term is being multiplied by itself It is the base

Step 2 Count the number of times the repeated term is in the expression (006) (006) (006) (006)

1 2 3 4 The repeated term is included 4 times The exponent is 4

Step 3 Write the exponential expression

Put the base within parentheses Put the exponent outside (006)4

Answer (006) (006) (006) (006) = (006)4

copy 2002 Renaissance Learning Inc

Write as a power

(17) (17) (17)

Step 1 Identify the term that is multiplied repeatedly

is the base

Step 2 Count the number of times the repeated term is in the expression

___ is the exponent

Step 3 Write the exponential expression

Answer (17)(17)(17) = ___

California

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4x2y

[ Simplify -52 + (-3)3 - 14

Step 1 Simplify the exponents

Remember that a negative sign stays with a number if the negative sign is included within parentheses The exponent tells you the number of times to multiply the number - 52 = - (5 5) = - 25 (_ 3)3 = (-3middot -3middot -3) = -27 14 = 1 1 1 1 = 1

-52 + (-3)3 - 14 -25 + -27 - 1

Step 2 Simplify from left to right -25 + -27 - 1

-52 - 1 = -53

Answer _52 + (~3)3 - 14 = -53


I Simplify~ -42 - (_2)4 + (-1)3


-42 =

(_2)4 =

(-1)3 =

-42 (_2)4 + (_1)3

------- + ------ shy

Step 2 Simplify from left to right

Answer -42 - (_2)4 + (-1)3 = ________ _

California

4x2y

(5)Simplify 6 - 3

Step 1 Review negative exponents

Negative exponents tell you to take the reciprocal of the number being raised to a power

(ifl = (if (~) - 2 = Gf

Step 2 Take the reciprocal of the number being raised to a negative power

(~r3 = (~r

Step 3 Write the product without the exponent and multiply

(~r = ~ ~ ~ = i~~

(5)-3 216Answer 6 = 125


ISimplify

Step 1

Step 2

Step 3

Answer

( ~r Review negative exponents

To drop the negative sign on the exponent how should the number being raised to a power change

Take the reciprocal of the number being raised to a negative power

(~) -2= __

Write the product without the exponent and multiply

(9)2 - 2 = _____

California bull

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4x2y Tnrn

ISimplify ( - 8)1

Step 1 Review fractional exponents

The denominator of a fractional exponent tells you what root to take Two in the denominator tells you to take the square root of the number Three in the denominator tells you to take the cube or third root of the number

The numerator of a fractional exponent works the same as a whole number exponent

3 8 3 b -3 38bB a - = -ya = -yo

Step 2 Rewrite the expression as a radical

2~ (-8)3~ (_8)2

Step 3 Take the root of the number

-2middot -2middot -2 = -8 -8 = -2

(_ 8)2 = (_ 2)2

Step 4 Raise the number to a power

( - 2) 2 = - 2 - 2 = 4

2

Answer (-8)3 = 4


I~impify (lOo)l


The denominator of a fractional exponent tells you

The numerator of a fractional exponent works the

same as __________________

Write the following as radical expressions 5 7

4 = 25 2 =

Step 2 Rewrite the expression as a radical 3

(100) 2 = ____



3

Answer (100) 2 = _____

California

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4x2y

I (55 23 48)5Simplify 56 25 43

74 39 bull 22 Simplify (710 bull 38 bull 25)I

- shy 4 1

Step 1 Review properties of exponents Step 1 Review properties of exponents When exponential expressions have the same base When dividing exponential terms that have the same the exponents can be simplified

base the exponents When dividing exponential terms exponents on the same base can be subtracted

When a power is raised to a power 55 = 5(5 - 2) = 53 52 = 5(2-5) = 5 - 3 = l ~ ~ ~

____________ the exponents When an exponential term is raised to a power multiply the two exponents (53)5 = 5(35) = 515

Step 2 Simplify the fraction Step 2 Simplify the fraction 23 485523 48 _ 55 25 43562543 - 56 74 39 22

55 _ 5(5 - 6) _ 5- 1 _ 1 710 38 bull 25 6 - - - 5

5

23 (3 - 5) -2 L Simplify each individual fraction 25 = 2 = 2 = 22

~ _ (8 - 3)

43 - 4 =45

45552348 _ 56 25 43 - 5middot 22

Step 3 Raise the fraction to a power Step 3 Raise the fraction to a power 5 425552348)5 = (4 )5(---L)5=

( 56 25 43 5 22 (5 22)5 55~1O 74 3922)4 _ = ( 710 38 25

25 9Answer (74 3 22)4 _Answer (55 23 48 )5 = _455 210562543 710 38 25 shy

copy 2002 Renaissance Learning Inc California

4x2y I TII1111

Rewrite x-s using only positive exponents


Negative exponents tell you to take the reciprocal of a number When a variable has a negative exponent you can change it to positive exponent by changing where it is in a fraction

5 3 3_5_ 2(pound = 5a a-3 1

5a-3 = ~ a3

When you move a term with a negative exponent to the opposite part of the fraction drop the negative sign

Step 2 Rewrite the expression using only positive exponents

x-S - 1 - x-s

Rewrite ~ using only positive exponents x


When you switch a term with a negative exponent from the numerator to the denominator of a fraction

_______ the negative sign on the exponent


1_ x- 8


4x2y IMultiply (3x 3yS) (7x)

Ffnrn

Step 1 Simplify exponents with the same base

The two x-terms can be combined They are exponential expressions with the same base The exponents can be added The two y-terms can be combined too

x 3 bull X = (xmiddot x x) x = X(3 + 1) = X4

lmiddoty2= (yyyyy)(yy) = y(S+ 2) = y7

Step 2 Multiply the whole numbers and write the new monomial

3middot7 = 21 (3x 3yS) (7x) = 21x4y7

lMultiply

Step 1

Step 2

(5x 4y) (~7)

Simplify exponents with the same base

X4 bull x 7 = x(- + --) - x

y y3 = ylt- + -) = Y

Multiply the whole numbers and write the new monomial

5middot4= ___

(5x 4y)(4x 7y) = --------shy


-- - -- --

---------------------------

4x2Y Objective-Multiply algebraic expressions with fractional oxponent

1 7 1~ 1 ] Multiply x

-

5 (X -

10 + X -2 ) Multiply x 3 (x 6 + x 4 )

Step 1 Use the distributive property

Multiply the term outside the parentheses by the Step 1 Use the distributive property

Multiply the term outside the parentheses by the terms inside the parentheses terms inside the parentheses 213 21 23 1 7 1

X 3 (X 6 + X 4) ~ X 3 (X 6 ) + X 3 (X 4

) X 5 (x 10 + x 2) = _______________

Step 2 Combine exponential terms having the same base Step 2 Combine exponential terms having the same base 2 1

The x terms in x 3 (x 6) can be combined because the exponents have the same base x Combine the terms by adding the fractions

~ 1 (2 1) ~] (2 1)X 3 (x 6) =X 3 + 6 X 3 (x 4) = x 3 + 4

~ + 1 ~ + J3 6 3 4

5 8 9 17plusmn + 16 6 6 12 + 12 12

(2 1) 5 (

2 3) 17 X 3 + 6 = X 6 X3+4 =X12

ll Answer x 3 (x 6 + X 4) = X 6 + X 12

~ 1 ~ 11 Answer X S (x 10 + x 2 ) =


4x2y ETIT

Simplify - 24ily2 - 8X5y 8

Step 1 Simplify exponents with the same bases

The two x-terms can be combined Since the terms are being divided the exponents can be subtracted The two y-terms can be combined too

3x x yenX x5 = x yenX xmiddot x

(3 - 5) -2 1 = x = x = x2

y2 _ ~ -1 ys y y Y 5-5 y y Y

(2 - 8) - 6 1 =y =y = (y

Step 2 Divide the whole numbers and write the new monomial

-24 - 3-8 shy

-24ily2 _ 3 ~6_~y8 shyx-y


-30X5y7

Simplify 5 x 8y 3


-x5 - (-- shyx8

- X --)

(---)-r=y = Y _____

Step 2 Divide the whole numbers and write the new monomiaL

-30-5shy

-30xY 5X 8y 3

California

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4x2y

-IS 4 - 1242x y z Simplify --6x 4y7z6

Step 1 Make all exponents positive

To change a negative exponent to a positive exponent switch it to the other part of the fraction Make sure to move its base too

3x --3 3ysFor example -=-5 -3

Y x In this monomial move the x- and z-terms in the numerator to the denominator Move the x-term in the denominator to the numerator 42x - ISy 4z - 12 42x4l

-6x 4z6 - -6XISz6z12

Step 2 Simplify exponents that have the same base and are being multiplied Add the exponents Z6Z 12 = Z(6 + 12) = Zl8

42x4l 42x4l -6xlSy7izl2 - -6x ISz I8

Step 3 Simplify exponents that have the same base and are being divided

= x-llSubtract the exponents xs = X(4 - IS) = --h x x

L (4 -7) -3 1 7 =y =y =-3

Y Y 42x4y4 42

-6x 15 y 7z18 -6x lliz l8


~ -~7-6 shy

42x- 15lz-12 -7 -6x-4i xllizl8


18x7y - 8z- 9 ~ Simplify 3x-4y 5 6z I


Which terms in the numerator should be moved to the

denominator

Which terms in the denominator should be moved to

the numerator _______

18x7y - 8z- 9

- 4 -5- 6 3x Y z

Step 2 Simplify exponents that have the same base and are being multiplied



California

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4x2y

[ Simplify (-5b4c-8d 3) - 2

Step 1 Raise each term to the power outside the parentheses

(_ 5b4c-8d3) -2 = (_ 5) - 2 (b4) - 2 (C- II) - 2 (d 3) -2

Step 2 Simplify powers raised to powers

Remember that you can simplify powers raised to powers by multiplying (-5) -2 (b 4) - 2 (C - 8r-2 (d 3) - 2

(-5) -2 b-8 bull C16 bull d- 6 = (-5) -2b -8CI6d-6


Put negative exponents in the denominator of a fraction

16C middotI6d-6(-5) -2b- IlC = (-5)2 8 6

b d

Step 4 Simplify any remaining numerical terms

(-5)2 = 25 16 16

C C8 6(-5)2 b8d6 25b d

Answer (-5b4c-8d 3)-2 = ~ d 625b ll

6ISimplify (3b - c2d 5r-3


(3b -6C 2d 5 ) - 3 =




Answer (3b - 6C2d 5 ) - 3 =

copy 2U02 Renaissance Learning Inc California

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4x2y

bull (8b3c10d - 5 ) - 4

SImplify (2b6c -4d 3) - 5

Step 1 Raise the numerator and the denominator to the power outside the parentheses (8b3c10d ~ 5)-4 8-4b-12c- 40d20

(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15

Step 2 Make all exponents positive Switch bases with negative exponents to the opposite part of the fraction

8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200


2 15 35Add the exponents d 0d = d(20+ 15) = d

c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18

Subtract the exponents b12 = b = b

25b30d35 25b18d35

84b12 60 84 60 c c

Step 5 Simplify any remaining numerical terms 25 32 1 84 = 4096 = 128

25b18d35 b18d 35

84 60c 128c60

(8b3c10d - 5) - 4 bUli~5 Answer

(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3

ISimplify (5b - 3c5d 2) 4

Step 1 Raise the numerator and the denominator to the power outside the parentheses

(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

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4x2y

Write 10470000 in scientific notation Write 34 x 10-4 in decimal notation

Step 1 Determine the decimal to use to write a number in scientific notation

A number in scientific notation has one whole number with the remaining non-zero digits written after the decimal point Drop all zeros after the final non-zero digit in numbers greater than zero Drop all zeros before the first non-zero digit in numbers between 0 and 1

In 10470000 the last non-zero digit when you read from left to right is 7 Keep zeros between non-zero digits

The decimal to use is 1047

Step 2 Determine the exponent on 10

Ask yourself How many places would I have to move the decimal point to get it back to its original position 1~ 10470000

The decimal will move 7 places Use 7 as the exponent Since the original number is greater than 0 the exponent is positive

104 70000 = 1047 x 107

Please turn the card over for the rest of the problem

Write 000000107 in scientific notation Write 4501 x lOG in decimal notation


The first non-zero digit is

The decimal to use is ~~~~-


How many places would you have to move the decimal

point to get it back to its original position

Since the original number is than 0 the

exponent is

000000107 = ______


------

--------

----------------


Write 000000107 in scientific notation Write 4501 x 10ri in decimal notation

Step 3 Determine the direction the decimal point moves when you change a number in scientific notation back to decimal form The exponent on 10 in 34 x 10-

4 is negative Move

the decimal point to the left When the exponent is positive move the decimal point to the right

Step 4 Move the decimal point the number of places indicated by the exponent

For 34 x 10-4 move the decimal point 4 places

to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034


Step 3 Determine the direction the decimal point moves when you change a number in scientific notation back to decimal form

The exponent on 10 in 4501 x 106 is

Move the decimal point to the


For 4501 x 106 move the decimal point

1064501 X =

California

4x2y

Simplify and express in scientific notation (14 x 104) (76 x 10 - 3)

(25 x 10 - 2)

Step 1 Use the commutative property of multiplication to simplify the numerator

This helps you put like numbers together (14 x 104) (76 x 10-3

) = (14 x 76) (104 x 10-3)

Step 2 Use the product of powers property 104 x 10- 3 = 10(4 + -3) = 101

Multiply the decimals as you normally would (14 x 76) x (104 x 10- 3

) = 1064 x 101

Step 3 Use the quotient of powers property to simplify the fraction

Wi --- 10-2 = 10(1 - - 2) = 103

Divide the decimals as you normally would

1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)

Simplify and express in scientific notation 2 3

(74 x 10 ) (50 X 10 )

(80 x 10 - 4)


Step 2 Use the product of powers property

Multiply the decimals as you normally would



1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn

Last year a large trucking company delivered about 08 million tons of goods at an average value of $25100 per ton What was the total value of goods delivered Express your answer in scientific notation

Step 1 Write numbers in scientific notation

1 million =1000000 10508 million = 800000 = 8 X

104

25100 = 251 x

Step 2 Write the problem to be solved

Describe the problem with smaller numbers to help you determine which operation to use

Suppose the problem is about delivering 2 truckloads of goods worth $500 each 2 truckloads at $500 each = 2 x $500 = $1000 Use multiplication to solve this problem (8 x 105

) x (251 X 104)

Step 3 Use what you know about exponents to compute (8 x 10~ x (251 X 104

) = (8 x 251) x (105 x 104)

10 9 = 2008 X

This number is not in scientific notation since the number in front of the decimal is greater than nine 2008 x 10 9 = 2008 X 1010

Step 4 Answer the question

The trucking company delivered goods worth $2008 x 1010


Ms Z a pop singer released a new CD in November Sales were 27 million In December sales decreased to 04 million How many times more sales were made in November than in December


27 million = ______________

04 million = ______________


Which operation is needed

Step 3 Use what you know about exponents to compute


California

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4x2y

[ Simplify -52 + (-3)3 - 14


Remember that a negative sign stays with a number if the negative sign is included within parentheses The exponent tells you the number of times to multiply the number - 52 = - (5 5) = - 25 (_ 3)3 = (-3middot -3middot -3) = -27 14 = 1 1 1 1 = 1

-52 + (-3)3 - 14 -25 + -27 - 1

Step 2 Simplify from left to right -25 + -27 - 1

-52 - 1 = -53

Answer _52 + (~3)3 - 14 = -53


I Simplify~ -42 - (_2)4 + (-1)3


-42 =

(_2)4 =

(-1)3 =

-42 (_2)4 + (_1)3

------- + ------ shy

Step 2 Simplify from left to right

Answer -42 - (_2)4 + (-1)3 = ________ _

California

4x2y

(5)Simplify 6 - 3



(ifl = (if (~) - 2 = Gf


(~r3 = (~r


(~r = ~ ~ ~ = i~~

(5)-3 216Answer 6 = 125


ISimplify

Step 1

Step 2

Step 3

Answer




(~) -2= __


(9)2 - 2 = _____

California bull

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4x2y Tnrn

ISimplify ( - 8)1




3 8 3 b -3 38bB a - = -ya = -yo


2~ (-8)3~ (_8)2


-2middot -2middot -2 = -8 -8 = -2

(_ 8)2 = (_ 2)2


( - 2) 2 = - 2 - 2 = 4

2

Answer (-8)3 = 4


I~impify (lOo)l




same as __________________


4 = 25 2 =


(100) 2 = ____



3

Answer (100) 2 = _____

California

- ----

4x2y

I (55 23 48)5Simplify 56 25 43


- shy 4 1






55 _ 5(5 - 6) _ 5- 1 _ 1 710 38 bull 25 6 - - - 5

5


~ _ (8 - 3)

43 - 4 =45

45552348 _ 56 25 43 - 5middot 22


( 56 25 43 5 22 (5 22)5 55~1O 74 3922)4 _ = ( 710 38 25



4x2y I TII1111




5 3 3_5_ 2(pound = 5a a-3 1

5a-3 = ~ a3



x-S - 1 - x-s






1_ x- 8



Ffnrn






3middot7 = 21 (3x 3yS) (7x) = 21x4y7

lMultiply

Step 1

Step 2

(5x 4y) (~7)


X4 bull x 7 = x(- + --) - x

y y3 = ylt- + -) = Y


5middot4= ___

(5x 4y)(4x 7y) = --------shy


-- - -- --

---------------------------



-

5 (X -

10 + X -2 ) Multiply x 3 (x 6 + x 4 )




X 3 (X 6 + X 4) ~ X 3 (X 6 ) + X 3 (X 4

) X 5 (x 10 + x 2) = _______________



~ 1 (2 1) ~] (2 1)X 3 (x 6) =X 3 + 6 X 3 (x 4) = x 3 + 4

~ + 1 ~ + J3 6 3 4

5 8 9 17plusmn + 16 6 6 12 + 12 12

(2 1) 5 (

2 3) 17 X 3 + 6 = X 6 X3+4 =X12

ll Answer x 3 (x 6 + X 4) = X 6 + X 12

~ 1 ~ 11 Answer X S (x 10 + x 2 ) =


4x2y ETIT





(3 - 5) -2 1 = x = x = x2

y2 _ ~ -1 ys y y Y 5-5 y y Y

(2 - 8) - 6 1 =y =y = (y


-24 - 3-8 shy

-24ily2 _ 3 ~6_~y8 shyx-y


-30X5y7

Simplify 5 x 8y 3


-x5 - (-- shyx8

- X --)

(---)-r=y = Y _____


-30-5shy

-30xY 5X 8y 3

California

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4x2y






-6x 4z6 - -6XISz6z12





L (4 -7) -3 1 7 =y =y =-3

Y Y 42x4y4 42

-6x 15 y 7z18 -6x lliz l8


~ -~7-6 shy

42x- 15lz-12 -7 -6x-4i xllizl8





denominator



18x7y - 8z- 9

- 4 -5- 6 3x Y z




California

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4x2y



(_ 5b4c-8d3) -2 = (_ 5) - 2 (b4) - 2 (C- II) - 2 (d 3) -2






16C middotI6d-6(-5) -2b- IlC = (-5)2 8 6

b d


(-5)2 = 25 16 16

C C8 6(-5)2 b8d6 25b d

Answer (-5b4c-8d 3)-2 = ~ d 625b ll



(3b -6C 2d 5 ) - 3 =




Answer (3b - 6C2d 5 ) - 3 =


------------------------

4x2y

bull (8b3c10d - 5 ) - 4



(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15


8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200



c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18


25b30d35 25b18d35

84b12 60 84 60 c c


25b18d35 b18d 35

84 60c 128c60


(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3



(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

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4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

4x2y

(5)Simplify 6 - 3



(ifl = (if (~) - 2 = Gf


(~r3 = (~r


(~r = ~ ~ ~ = i~~

(5)-3 216Answer 6 = 125


ISimplify

Step 1

Step 2

Step 3

Answer




(~) -2= __


(9)2 - 2 = _____

California bull

----- -----

4x2y Tnrn

ISimplify ( - 8)1




3 8 3 b -3 38bB a - = -ya = -yo


2~ (-8)3~ (_8)2


-2middot -2middot -2 = -8 -8 = -2

(_ 8)2 = (_ 2)2


( - 2) 2 = - 2 - 2 = 4

2

Answer (-8)3 = 4


I~impify (lOo)l




same as __________________


4 = 25 2 =


(100) 2 = ____



3

Answer (100) 2 = _____

California

- ----

4x2y

I (55 23 48)5Simplify 56 25 43


- shy 4 1






55 _ 5(5 - 6) _ 5- 1 _ 1 710 38 bull 25 6 - - - 5

5


~ _ (8 - 3)

43 - 4 =45

45552348 _ 56 25 43 - 5middot 22


( 56 25 43 5 22 (5 22)5 55~1O 74 3922)4 _ = ( 710 38 25



4x2y I TII1111




5 3 3_5_ 2(pound = 5a a-3 1

5a-3 = ~ a3



x-S - 1 - x-s






1_ x- 8



Ffnrn






3middot7 = 21 (3x 3yS) (7x) = 21x4y7

lMultiply

Step 1

Step 2

(5x 4y) (~7)


X4 bull x 7 = x(- + --) - x

y y3 = ylt- + -) = Y


5middot4= ___

(5x 4y)(4x 7y) = --------shy


-- - -- --

---------------------------



-

5 (X -

10 + X -2 ) Multiply x 3 (x 6 + x 4 )




X 3 (X 6 + X 4) ~ X 3 (X 6 ) + X 3 (X 4

) X 5 (x 10 + x 2) = _______________



~ 1 (2 1) ~] (2 1)X 3 (x 6) =X 3 + 6 X 3 (x 4) = x 3 + 4

~ + 1 ~ + J3 6 3 4

5 8 9 17plusmn + 16 6 6 12 + 12 12

(2 1) 5 (

2 3) 17 X 3 + 6 = X 6 X3+4 =X12

ll Answer x 3 (x 6 + X 4) = X 6 + X 12

~ 1 ~ 11 Answer X S (x 10 + x 2 ) =


4x2y ETIT





(3 - 5) -2 1 = x = x = x2

y2 _ ~ -1 ys y y Y 5-5 y y Y

(2 - 8) - 6 1 =y =y = (y


-24 - 3-8 shy

-24ily2 _ 3 ~6_~y8 shyx-y


-30X5y7

Simplify 5 x 8y 3


-x5 - (-- shyx8

- X --)

(---)-r=y = Y _____


-30-5shy

-30xY 5X 8y 3

California

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4x2y






-6x 4z6 - -6XISz6z12





L (4 -7) -3 1 7 =y =y =-3

Y Y 42x4y4 42

-6x 15 y 7z18 -6x lliz l8


~ -~7-6 shy

42x- 15lz-12 -7 -6x-4i xllizl8





denominator



18x7y - 8z- 9

- 4 -5- 6 3x Y z




California

---

4x2y



(_ 5b4c-8d3) -2 = (_ 5) - 2 (b4) - 2 (C- II) - 2 (d 3) -2






16C middotI6d-6(-5) -2b- IlC = (-5)2 8 6

b d


(-5)2 = 25 16 16

C C8 6(-5)2 b8d6 25b d

Answer (-5b4c-8d 3)-2 = ~ d 625b ll



(3b -6C 2d 5 ) - 3 =




Answer (3b - 6C2d 5 ) - 3 =


------------------------

4x2y

bull (8b3c10d - 5 ) - 4



(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15


8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200



c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18


25b30d35 25b18d35

84b12 60 84 60 c c


25b18d35 b18d 35

84 60c 128c60


(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3



(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

-----

----

--------

4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

----- -----

4x2y Tnrn

ISimplify ( - 8)1




3 8 3 b -3 38bB a - = -ya = -yo


2~ (-8)3~ (_8)2


-2middot -2middot -2 = -8 -8 = -2

(_ 8)2 = (_ 2)2


( - 2) 2 = - 2 - 2 = 4

2

Answer (-8)3 = 4


I~impify (lOo)l




same as __________________


4 = 25 2 =


(100) 2 = ____



3

Answer (100) 2 = _____

California

- ----

4x2y

I (55 23 48)5Simplify 56 25 43


- shy 4 1






55 _ 5(5 - 6) _ 5- 1 _ 1 710 38 bull 25 6 - - - 5

5


~ _ (8 - 3)

43 - 4 =45

45552348 _ 56 25 43 - 5middot 22


( 56 25 43 5 22 (5 22)5 55~1O 74 3922)4 _ = ( 710 38 25



4x2y I TII1111




5 3 3_5_ 2(pound = 5a a-3 1

5a-3 = ~ a3



x-S - 1 - x-s






1_ x- 8



Ffnrn






3middot7 = 21 (3x 3yS) (7x) = 21x4y7

lMultiply

Step 1

Step 2

(5x 4y) (~7)


X4 bull x 7 = x(- + --) - x

y y3 = ylt- + -) = Y


5middot4= ___

(5x 4y)(4x 7y) = --------shy


-- - -- --

---------------------------



-

5 (X -

10 + X -2 ) Multiply x 3 (x 6 + x 4 )




X 3 (X 6 + X 4) ~ X 3 (X 6 ) + X 3 (X 4

) X 5 (x 10 + x 2) = _______________



~ 1 (2 1) ~] (2 1)X 3 (x 6) =X 3 + 6 X 3 (x 4) = x 3 + 4

~ + 1 ~ + J3 6 3 4

5 8 9 17plusmn + 16 6 6 12 + 12 12

(2 1) 5 (

2 3) 17 X 3 + 6 = X 6 X3+4 =X12

ll Answer x 3 (x 6 + X 4) = X 6 + X 12

~ 1 ~ 11 Answer X S (x 10 + x 2 ) =


4x2y ETIT





(3 - 5) -2 1 = x = x = x2

y2 _ ~ -1 ys y y Y 5-5 y y Y

(2 - 8) - 6 1 =y =y = (y


-24 - 3-8 shy

-24ily2 _ 3 ~6_~y8 shyx-y


-30X5y7

Simplify 5 x 8y 3


-x5 - (-- shyx8

- X --)

(---)-r=y = Y _____


-30-5shy

-30xY 5X 8y 3

California

-------

4x2y






-6x 4z6 - -6XISz6z12





L (4 -7) -3 1 7 =y =y =-3

Y Y 42x4y4 42

-6x 15 y 7z18 -6x lliz l8


~ -~7-6 shy

42x- 15lz-12 -7 -6x-4i xllizl8





denominator



18x7y - 8z- 9

- 4 -5- 6 3x Y z




California

---

4x2y



(_ 5b4c-8d3) -2 = (_ 5) - 2 (b4) - 2 (C- II) - 2 (d 3) -2






16C middotI6d-6(-5) -2b- IlC = (-5)2 8 6

b d


(-5)2 = 25 16 16

C C8 6(-5)2 b8d6 25b d

Answer (-5b4c-8d 3)-2 = ~ d 625b ll



(3b -6C 2d 5 ) - 3 =




Answer (3b - 6C2d 5 ) - 3 =


------------------------

4x2y

bull (8b3c10d - 5 ) - 4



(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15


8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200



c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18


25b30d35 25b18d35

84b12 60 84 60 c c


25b18d35 b18d 35

84 60c 128c60


(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3



(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

-----

----

--------

4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

- ----

4x2y

I (55 23 48)5Simplify 56 25 43


- shy 4 1






55 _ 5(5 - 6) _ 5- 1 _ 1 710 38 bull 25 6 - - - 5

5


~ _ (8 - 3)

43 - 4 =45

45552348 _ 56 25 43 - 5middot 22


( 56 25 43 5 22 (5 22)5 55~1O 74 3922)4 _ = ( 710 38 25



4x2y I TII1111




5 3 3_5_ 2(pound = 5a a-3 1

5a-3 = ~ a3



x-S - 1 - x-s






1_ x- 8



Ffnrn






3middot7 = 21 (3x 3yS) (7x) = 21x4y7

lMultiply

Step 1

Step 2

(5x 4y) (~7)


X4 bull x 7 = x(- + --) - x

y y3 = ylt- + -) = Y


5middot4= ___

(5x 4y)(4x 7y) = --------shy


-- - -- --

---------------------------



-

5 (X -

10 + X -2 ) Multiply x 3 (x 6 + x 4 )




X 3 (X 6 + X 4) ~ X 3 (X 6 ) + X 3 (X 4

) X 5 (x 10 + x 2) = _______________



~ 1 (2 1) ~] (2 1)X 3 (x 6) =X 3 + 6 X 3 (x 4) = x 3 + 4

~ + 1 ~ + J3 6 3 4

5 8 9 17plusmn + 16 6 6 12 + 12 12

(2 1) 5 (

2 3) 17 X 3 + 6 = X 6 X3+4 =X12

ll Answer x 3 (x 6 + X 4) = X 6 + X 12

~ 1 ~ 11 Answer X S (x 10 + x 2 ) =


4x2y ETIT





(3 - 5) -2 1 = x = x = x2

y2 _ ~ -1 ys y y Y 5-5 y y Y

(2 - 8) - 6 1 =y =y = (y


-24 - 3-8 shy

-24ily2 _ 3 ~6_~y8 shyx-y


-30X5y7

Simplify 5 x 8y 3


-x5 - (-- shyx8

- X --)

(---)-r=y = Y _____


-30-5shy

-30xY 5X 8y 3

California

-------

4x2y






-6x 4z6 - -6XISz6z12





L (4 -7) -3 1 7 =y =y =-3

Y Y 42x4y4 42

-6x 15 y 7z18 -6x lliz l8


~ -~7-6 shy

42x- 15lz-12 -7 -6x-4i xllizl8





denominator



18x7y - 8z- 9

- 4 -5- 6 3x Y z




California

---

4x2y



(_ 5b4c-8d3) -2 = (_ 5) - 2 (b4) - 2 (C- II) - 2 (d 3) -2






16C middotI6d-6(-5) -2b- IlC = (-5)2 8 6

b d


(-5)2 = 25 16 16

C C8 6(-5)2 b8d6 25b d

Answer (-5b4c-8d 3)-2 = ~ d 625b ll



(3b -6C 2d 5 ) - 3 =




Answer (3b - 6C2d 5 ) - 3 =


------------------------

4x2y

bull (8b3c10d - 5 ) - 4



(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15


8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200



c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18


25b30d35 25b18d35

84b12 60 84 60 c c


25b18d35 b18d 35

84 60c 128c60


(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3



(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

-----

----

--------

4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

4x2y I TII1111




5 3 3_5_ 2(pound = 5a a-3 1

5a-3 = ~ a3



x-S - 1 - x-s






1_ x- 8



Ffnrn






3middot7 = 21 (3x 3yS) (7x) = 21x4y7

lMultiply

Step 1

Step 2

(5x 4y) (~7)


X4 bull x 7 = x(- + --) - x

y y3 = ylt- + -) = Y


5middot4= ___

(5x 4y)(4x 7y) = --------shy


-- - -- --

---------------------------



-

5 (X -

10 + X -2 ) Multiply x 3 (x 6 + x 4 )




X 3 (X 6 + X 4) ~ X 3 (X 6 ) + X 3 (X 4

) X 5 (x 10 + x 2) = _______________



~ 1 (2 1) ~] (2 1)X 3 (x 6) =X 3 + 6 X 3 (x 4) = x 3 + 4

~ + 1 ~ + J3 6 3 4

5 8 9 17plusmn + 16 6 6 12 + 12 12

(2 1) 5 (

2 3) 17 X 3 + 6 = X 6 X3+4 =X12

ll Answer x 3 (x 6 + X 4) = X 6 + X 12

~ 1 ~ 11 Answer X S (x 10 + x 2 ) =


4x2y ETIT





(3 - 5) -2 1 = x = x = x2

y2 _ ~ -1 ys y y Y 5-5 y y Y

(2 - 8) - 6 1 =y =y = (y


-24 - 3-8 shy

-24ily2 _ 3 ~6_~y8 shyx-y


-30X5y7

Simplify 5 x 8y 3


-x5 - (-- shyx8

- X --)

(---)-r=y = Y _____


-30-5shy

-30xY 5X 8y 3

California

-------

4x2y






-6x 4z6 - -6XISz6z12





L (4 -7) -3 1 7 =y =y =-3

Y Y 42x4y4 42

-6x 15 y 7z18 -6x lliz l8


~ -~7-6 shy

42x- 15lz-12 -7 -6x-4i xllizl8





denominator



18x7y - 8z- 9

- 4 -5- 6 3x Y z




California

---

4x2y



(_ 5b4c-8d3) -2 = (_ 5) - 2 (b4) - 2 (C- II) - 2 (d 3) -2






16C middotI6d-6(-5) -2b- IlC = (-5)2 8 6

b d


(-5)2 = 25 16 16

C C8 6(-5)2 b8d6 25b d

Answer (-5b4c-8d 3)-2 = ~ d 625b ll



(3b -6C 2d 5 ) - 3 =




Answer (3b - 6C2d 5 ) - 3 =


------------------------

4x2y

bull (8b3c10d - 5 ) - 4



(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15


8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200



c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18


25b30d35 25b18d35

84b12 60 84 60 c c


25b18d35 b18d 35

84 60c 128c60


(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3



(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

-----

----

--------

4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California


Ffnrn






3middot7 = 21 (3x 3yS) (7x) = 21x4y7

lMultiply

Step 1

Step 2

(5x 4y) (~7)


X4 bull x 7 = x(- + --) - x

y y3 = ylt- + -) = Y


5middot4= ___

(5x 4y)(4x 7y) = --------shy


-- - -- --

---------------------------



-

5 (X -

10 + X -2 ) Multiply x 3 (x 6 + x 4 )




X 3 (X 6 + X 4) ~ X 3 (X 6 ) + X 3 (X 4

) X 5 (x 10 + x 2) = _______________



~ 1 (2 1) ~] (2 1)X 3 (x 6) =X 3 + 6 X 3 (x 4) = x 3 + 4

~ + 1 ~ + J3 6 3 4

5 8 9 17plusmn + 16 6 6 12 + 12 12

(2 1) 5 (

2 3) 17 X 3 + 6 = X 6 X3+4 =X12

ll Answer x 3 (x 6 + X 4) = X 6 + X 12

~ 1 ~ 11 Answer X S (x 10 + x 2 ) =


4x2y ETIT





(3 - 5) -2 1 = x = x = x2

y2 _ ~ -1 ys y y Y 5-5 y y Y

(2 - 8) - 6 1 =y =y = (y


-24 - 3-8 shy

-24ily2 _ 3 ~6_~y8 shyx-y


-30X5y7

Simplify 5 x 8y 3


-x5 - (-- shyx8

- X --)

(---)-r=y = Y _____


-30-5shy

-30xY 5X 8y 3

California

-------

4x2y






-6x 4z6 - -6XISz6z12





L (4 -7) -3 1 7 =y =y =-3

Y Y 42x4y4 42

-6x 15 y 7z18 -6x lliz l8


~ -~7-6 shy

42x- 15lz-12 -7 -6x-4i xllizl8





denominator



18x7y - 8z- 9

- 4 -5- 6 3x Y z




California

---

4x2y



(_ 5b4c-8d3) -2 = (_ 5) - 2 (b4) - 2 (C- II) - 2 (d 3) -2






16C middotI6d-6(-5) -2b- IlC = (-5)2 8 6

b d


(-5)2 = 25 16 16

C C8 6(-5)2 b8d6 25b d

Answer (-5b4c-8d 3)-2 = ~ d 625b ll



(3b -6C 2d 5 ) - 3 =




Answer (3b - 6C2d 5 ) - 3 =


------------------------

4x2y

bull (8b3c10d - 5 ) - 4



(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15


8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200



c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18


25b30d35 25b18d35

84b12 60 84 60 c c


25b18d35 b18d 35

84 60c 128c60


(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3



(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

-----

----

--------

4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

-- - -- --

---------------------------



-

5 (X -

10 + X -2 ) Multiply x 3 (x 6 + x 4 )




X 3 (X 6 + X 4) ~ X 3 (X 6 ) + X 3 (X 4

) X 5 (x 10 + x 2) = _______________



~ 1 (2 1) ~] (2 1)X 3 (x 6) =X 3 + 6 X 3 (x 4) = x 3 + 4

~ + 1 ~ + J3 6 3 4

5 8 9 17plusmn + 16 6 6 12 + 12 12

(2 1) 5 (

2 3) 17 X 3 + 6 = X 6 X3+4 =X12

ll Answer x 3 (x 6 + X 4) = X 6 + X 12

~ 1 ~ 11 Answer X S (x 10 + x 2 ) =


4x2y ETIT





(3 - 5) -2 1 = x = x = x2

y2 _ ~ -1 ys y y Y 5-5 y y Y

(2 - 8) - 6 1 =y =y = (y


-24 - 3-8 shy

-24ily2 _ 3 ~6_~y8 shyx-y


-30X5y7

Simplify 5 x 8y 3


-x5 - (-- shyx8

- X --)

(---)-r=y = Y _____


-30-5shy

-30xY 5X 8y 3

California

-------

4x2y






-6x 4z6 - -6XISz6z12





L (4 -7) -3 1 7 =y =y =-3

Y Y 42x4y4 42

-6x 15 y 7z18 -6x lliz l8


~ -~7-6 shy

42x- 15lz-12 -7 -6x-4i xllizl8





denominator



18x7y - 8z- 9

- 4 -5- 6 3x Y z




California

---

4x2y



(_ 5b4c-8d3) -2 = (_ 5) - 2 (b4) - 2 (C- II) - 2 (d 3) -2






16C middotI6d-6(-5) -2b- IlC = (-5)2 8 6

b d


(-5)2 = 25 16 16

C C8 6(-5)2 b8d6 25b d

Answer (-5b4c-8d 3)-2 = ~ d 625b ll



(3b -6C 2d 5 ) - 3 =




Answer (3b - 6C2d 5 ) - 3 =


------------------------

4x2y

bull (8b3c10d - 5 ) - 4



(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15


8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200



c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18


25b30d35 25b18d35

84b12 60 84 60 c c


25b18d35 b18d 35

84 60c 128c60


(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3



(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

-----

----

--------

4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

4x2y ETIT





(3 - 5) -2 1 = x = x = x2

y2 _ ~ -1 ys y y Y 5-5 y y Y

(2 - 8) - 6 1 =y =y = (y


-24 - 3-8 shy

-24ily2 _ 3 ~6_~y8 shyx-y


-30X5y7

Simplify 5 x 8y 3


-x5 - (-- shyx8

- X --)

(---)-r=y = Y _____


-30-5shy

-30xY 5X 8y 3

California

-------

4x2y






-6x 4z6 - -6XISz6z12





L (4 -7) -3 1 7 =y =y =-3

Y Y 42x4y4 42

-6x 15 y 7z18 -6x lliz l8


~ -~7-6 shy

42x- 15lz-12 -7 -6x-4i xllizl8





denominator



18x7y - 8z- 9

- 4 -5- 6 3x Y z




California

---

4x2y



(_ 5b4c-8d3) -2 = (_ 5) - 2 (b4) - 2 (C- II) - 2 (d 3) -2






16C middotI6d-6(-5) -2b- IlC = (-5)2 8 6

b d


(-5)2 = 25 16 16

C C8 6(-5)2 b8d6 25b d

Answer (-5b4c-8d 3)-2 = ~ d 625b ll



(3b -6C 2d 5 ) - 3 =




Answer (3b - 6C2d 5 ) - 3 =


------------------------

4x2y

bull (8b3c10d - 5 ) - 4



(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15


8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200



c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18


25b30d35 25b18d35

84b12 60 84 60 c c


25b18d35 b18d 35

84 60c 128c60


(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3



(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

-----

----

--------

4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

-------

4x2y






-6x 4z6 - -6XISz6z12





L (4 -7) -3 1 7 =y =y =-3

Y Y 42x4y4 42

-6x 15 y 7z18 -6x lliz l8


~ -~7-6 shy

42x- 15lz-12 -7 -6x-4i xllizl8





denominator



18x7y - 8z- 9

- 4 -5- 6 3x Y z




California

---

4x2y



(_ 5b4c-8d3) -2 = (_ 5) - 2 (b4) - 2 (C- II) - 2 (d 3) -2






16C middotI6d-6(-5) -2b- IlC = (-5)2 8 6

b d


(-5)2 = 25 16 16

C C8 6(-5)2 b8d6 25b d

Answer (-5b4c-8d 3)-2 = ~ d 625b ll



(3b -6C 2d 5 ) - 3 =




Answer (3b - 6C2d 5 ) - 3 =


------------------------

4x2y

bull (8b3c10d - 5 ) - 4



(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15


8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200



c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18


25b30d35 25b18d35

84b12 60 84 60 c c


25b18d35 b18d 35

84 60c 128c60


(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3



(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

-----

----

--------

4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

---

4x2y



(_ 5b4c-8d3) -2 = (_ 5) - 2 (b4) - 2 (C- II) - 2 (d 3) -2






16C middotI6d-6(-5) -2b- IlC = (-5)2 8 6

b d


(-5)2 = 25 16 16

C C8 6(-5)2 b8d6 25b d

Answer (-5b4c-8d 3)-2 = ~ d 625b ll



(3b -6C 2d 5 ) - 3 =




Answer (3b - 6C2d 5 ) - 3 =


------------------------

4x2y

bull (8b3c10d - 5 ) - 4



(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15


8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200



c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18


25b30d35 25b18d35

84b12 60 84 60 c c


25b18d35 b18d 35

84 60c 128c60


(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3



(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

-----

----

--------

4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

------------------------

4x2y

bull (8b3c10d - 5 ) - 4



(2b6c - 4d3) -5 = 2 - 5b - 30C20d - 15


8-4b-12C-40d20 25b30d20d15

2 - 5b - 30C20d - 15 - 84b12C200



c20c40 = C(20 + 40) = COO

25b30d35

b12 60

25b30d20d15

84b12C2DC40 84C


b30 (30 - 12) 18


25b30d35 25b18d35

84b12 60 84 60 c c


25b18d35 b18d 35

84 60c 128c60


(2b6c --4d 3) -5 = 128c60


C (3b7c- 3r 2 ) - 3



(3b7c-3d- 2) - 3

(5b -- 3C5d-2) - 4 =





(3b7c- 3r 2 ) - 3 Answer (5b -3c5d - 2) - 4

California

-----

----

--------

4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

-----

----

--------

4x2y









104 70000 = 1047 x 107










exponent is

000000107 = ______


------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

------

--------

----------------




4 is negative Move




to the left

34 X 10-4

bull Ogqq~4

34 x 10-4 = 000034







1064501 X =

California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

4x2y


(25 x 10 - 2)



) = (14 x 76) (104 x 10-3)



) = 1064 x 101


Wi --- 10-2 = 10(1 - - 2) = 103


1064 x 101 = 4256 X 103 225 X 10 shy

(14 X 104) (76 x 10 ~ 3) = 4256 X 103

Answer (25 x 10 2)


(74 x 10 ) (50 X 10 )

(80 x 10 - 4)






1(74 X 102

) (50 x 10 )Answer (80 x 10

- 4 )


4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

4x2y Ernrn




104

25100 = 251 x




) x (251 X 104)


) = (8 x 251) x (105 x 104)

10 9 = 2008 X







27 million = ______________

04 million = ______________





California

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