November 09, 2011
Which one of these expressions is not a monomial?
5y
2
x
A monomial is:
8
- a constant 5
- a variable y
- a product 5y
x+y
9xy
x
It is a polynomial with only 1 term
To simplify an expression containing powers means to…
November 09, 2011
Properties Of Exponents
3
Multiplying Powers with the same base.
5
6 6
(6
b
6 6)(6 6 6 6 6)
7
5
b = b
What can I do with this?
f
2
4
h =
12
pull to the right
for answer
November 09, 2011
Multiplying monomials
(3x)(2x)
1
Multiply coeffients
= (3x)(2x)
2
Multiply variables
= (3)(2) (x)(x)
2
= (6) (x )
3
= 6x
2
Multiplying monomials: adding exponents
2
4
2
4
(5x )(2x )
1
= (5x )(2x )
4
2
2
= (5)(2)(x ) (x )
= (10)(x
3
= 10x
6
2+4
)
November 09, 2011
Practice multiplying monomials
3
6
2
(4xy ) (7x y )
(4y )(y )
=
4y
8
=
4 8
28x y
2
7
6
3
(3y )(y )(6x y)
(8x)(4y )
= 32xy
3 5
7
=
3 9
18x y
Fill in the blanks
(
(
2
x ) (7x
2
xy
) = 35x
)(4x
4
4
(abc)(2a b c ) (
5 3
8 7
13 12
y )(3x y ) = 60x y
5 3
4
6
a
2
bc
3
7 7 7
) = 2a b c
7 7 7
(abc)(2a b c ) (a bc ) =2a b c
November 09, 2011
Express the area and volume in terms of x
8x
x
5
1
x
3
20x
4x
2
2 2
A = 83 x or 2 3 x
A=
V=
Dividing Powers with the same Base
7
7
4
2
=
7777
7 7
V = 16x
3
November 09, 2011
OK, now that we have mul9plica9on down, let's take care of nega9ve exponents:
-­‐5
1) x = 2) ab
3) 4) -­‐2
November 09, 2011
Proof of negative exponents turning positive
Raising a power to a power - MULTIPLY
4
6
(8 ) = 8
3
(x )
-4
-7
-5
3 -7
= x
(n ) =
4 6
=8
24
November 09, 2011
Simplifying a product raised to a power:
1) (ab)
2
2 3 4
2) (w b )
5 -­‐2 -­‐7 -­‐2
3) (m q v )
Simplifying a quo9ent raised to a power:
1) 2) 3) November 09, 2011
November 09, 2011