Copyright©amberpasillas2010. Factored FormExponential Form x 8 y 8 x 8 2 x 2 y a b a 2 2a 2 b 1 13 p p p r r 13p 3 r 2

copyright©amberpasillas2010


Factored Form Exponential Formx • 8 • y • 8 • x 82x2y

a • b • a • 2 2a2b1

13 p p p r r 13p3r2


n n n n n

x3

x x x=

exponent

Base

When The Bases Are The Samexa

=xb xa + b

n3

=n2 n3 + 2Ex:

=

= n5

n5

ADD EXPONENTS!


1) 2)

3) 4)

5) 6)

4 5a a 5 8m m

2 53x x 3 62 4b b

4 23 (5 )n n 4 33 ( 2 )a a

9a 13m

73x 98b

615n 76a

HINT: Multiply coefficients

1


( )Power to Power Rule

xa

=b

xab

( )n3 2

(n n n)

Ex:

2= (n n n) (n n n) = n

6

= n3 2

= n6

When You Have an Exponent On The Outside of Parenthesis

MULTIPLY EXPONENTS!


1) 24x 8x 2) 248a 864a

3) 255x y 10 225x y 4) 34 22a b 12 68a b


Prime Numbers- A Prime number is a whole number with only 2 factors, one and itself.

Composite Numbers- A Composite number is a number that has more than two factors.

Example: 2, 3, 5, 7, 11, 13, 17…

Example: 4, 6, 8, 9, 10, 12, 14, 15…


Composite Number -Composite numbers can be written as the product of prime numbers. This is called:

Prime Factorization -Prime Factorization is the unique set of prime numbers whose product equals a given number.


Prime Factorization is when you write a

number as the product of prime numbers. Factor

Tree 36

36 2 2 3 3 2 236 2 3

2 18

2 9

3 3

Circle the

prime number

s


Write the prime factorization of the number 24.24 24

2 12

2 6

4 6

2 32 2

32 3 32 32 3

Circle the prime numbers

Notice you get the same answer doing it two different ways! No matter how your start, you will get the same answer!

That is why prime factorization is so unique!


96

2 48

6 8

96 2 2 2 2 2 3

2 3 2 4

2 2

Notice we put them in order from least to greatest

596 2 3


240

2 120

2 60

2 30

2 15

3 5

240 2 2 2 2 3 5 4240 2 3 5


9ab

9 ab

9ab 3 3 a b

a b3 3

Factor Form


6

26m 2 3 m m

26m2m

m m2 3

Factor Form


310

15

a

a=

2 5 a a a 3 5 a =

22

3

a

Write each expression in FACTOR FORM then simplify.


4

20

5

b

b=

2 2 5 b 5 b b b b

= 3

4

b



3

2

27a b

36ab=

3•3•3• • • •a a a b2• 2 •3•3• • •a b b =

23

4

a

b



1218

23

÷ 66

=

Simplify or Reduce this fraction.


1220

35

÷ 44

=



921

37

÷ 33

=


Take Out Your Study Guide!!!



#13

= x8+5

x8• x

5

(4a7b)

3 = 43a

7•3b

3

= x13

= 64a21

b3

Product of a Power Property

Power of a Power Property

= (-12)2(-3 • 4)

2

=144

Power of a Product Property

= (-12)(-12)


Prime Factorization is when you write a

number as the product of prime numbers. Factor Tree 36

#14

36 2 2 3 3 2 236 2 3

2 18

2 9

3 3

Circle the

prime numbers


Factoring#15

1)410m

15m=

2 5 m m m m 3 5 m =

32m

3

2)3

2

27a b

36ab=

3•3•3• • • •a a a b2• 2 •3•3• • •a b b =

23

4

a

b

12

2 6

2 3

2 2 3

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Copyright©amberpasillas2010. Factored FormExponential Form x 8 y 8 x 8 2 x 2 y a b a 2 2a 2 b 1 13 p p p r r 13p 3 r 2