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