Algebra 1A

Section 6.1: Multiplying Monomials

Warm-Up

22 = ______ ∙ ______ = ______

23 = ______ ∙ ______∙ ______ = ______

24 = ______ ∙ ______ ∙ ______∙ ______ = ______

32 = ______ ∙ ______ = ______

53 = ______ ∙ ______ ∙ ______ = ______

2 2 4

2 2 2 8

2 2 2 2 16

3 3 9

5 5 5 125

Important Concept

Power:__________________________________________

82 = ___________ NOT the same as _____________

X5 = _______________ NOT the same as __________

An exponent tells how many times we multiply the base by itself

8 x 8 8 x 2

x . x . x . x . x 5x

Example 1

(33)(32)

33 + 2 = 35

Example 2

(3x4y)(-4x2y)

3(-4)x6y2

-12x6y2

PRODUCT OF POWERS

· the base stays the __________________

· ____________ the exponents of the ___________________ base

____________________ the coefficients (number in front of the base)

same

Add

same

Multiply

Your Turn 1

(5y4)(3y)

15y5

Your Turn 2

(-4ab6)(-7a2b3)

28a3b9

6th hour

Please do on another piece of paper:

Example 1 Example 3Example 2

(3xy4)2

32x2y8

9x2y8

(-2xy4)3 (5ab4)3(3b2)2

(-2)3x3y12

-8x3y12

(5)3a3b12(3)2b4

(125a3b12)(9b4)

1125a3b16

Power of Powers

· _______________________ the exponents of the same ___________________

· raise the coefficient to the given __________________________

Multiply

base

power outside the parenthesis

Your Turn 1 Your Turn 3Your Turn 2

(2x2y)3 (-3xy4)4 (2xy)3(3x2)5

8x6y3 81x4y16 1944x13y3

Are you a master?

a) (x3)4 b) (42)(43) c) x3(x2)

d) (2xy2)3 e) 33 . 36 f) (-4m2n3)4

g) (-3a2b3)3 h) (n2)(n3)(n) i) (3xy)2(-2x2)3

Algebra 1A

Section 6.2: Dividing Monomials

Warm-Up

a) (42)(43) b) (4xy2)3

c) (n4)__ = n12 d) (______)2 = 81a2b4c10

45 = 1,024 43x3y6 = 48x3y6

3 9ab2c5

Example 1 Example 2 Example 3

4x5

2x3

4x3

8x8

78

72

2x2 1 2x5

76 or 117,649

4xxxxx2xxx

4xxx8xxxxxxxx

7777777777

DIVIDING MONOMIALS

 · ______________ the coefficients by

____________ or finding the

___________

· ___________ the exponents of the

______________ base

Divide

Reducing the fraction

decimal

Subtract

same

Your Turn 2Your Turn 1 Your Turn 3

10a3

5a 3b6 12b9

25

27

2a2 1 4b3

1 4

Example 4 Your Turn 4

144a2b5c 12a3bc3

-45x4y2z2

15x3y4z3

12b4

ac2

-3xy2z

When in doubt….right it out!

ARE YOU A MASTER????  

a) (a3b3)(a4b5) b) (-7g3h3)3 c) 510

57

d) e) f)

g) h) i)

Warm-up:

1. 2.

SECTION 6.3: DIVIDING MONOMIALS

I CAN . . .

simplify expressions with zero and negative exponents.

CAN YOU FIND THE PATTERN?42 43

32 33

22 23

12 13

02 03

12 13

22 23

32 33

42 43

ZERO EXPONENT PROPERTY

a) b) 06234 ba 0000,10

NEGATIVE EXPONENT PROPERTY

EX 1) Your Turn25

38

NEGATIVE EXPONENT PROPERTY

EX 2) Your Turn23 x 25 a

NEGATIVE EXPONENT PROPERTY

EX 3) Your Turn

4

2

7

14

b

ac

25

532

zx

zyx

ARE YOU A MASTER

a) b)0

7

122

24

54

yx

yx

cba

cba52

1234

4

12