Multiplying and Dividing Monomials

4.3

Monomial: • An expression that is either a:

(1) numeral or constant, ex : 5 (2)a variable, ex: x (3)or a product of numerals and variables ex: 5x (4)variables with whole number exponents. Ex: x²• If the monomial is a numeral, it is called a constant.• Excludes: “+”, “-”, and if exponent is negative or a

fraction.

4x3 x3 + 4

-8 2x2y y

12

1

x

ab75

2

1y

x3 means: x • x • x

x2 means: x • x

x3 • x2 means (x • x • x) •(x •x)x5

Multiplying Powers with the same base:

Xm • xn = xm+n

Simplify. Express using exponents.

84 • 83

84+3 = 87

Simplify. Express using exponents.

y • y2 • y6

y1+2+6 = y9

Multiply 2 monomials using “properties”

(3x • 4x) = (3 • 4)(x • x) = 12x2

(Associative and Commutative) Group the numbers together and then group the

same variables together(3x2)(-x) = (3x2)(-1x) = (3 • -1)(x2 •x)

= -3x3

(-7x2y5)(4xy3)

(-7 • 4)(x2 • x)(y5 • y3)

-28x3 y8

Simplify. Express using exponents.

(mn2) (m4n6)

m1+4 • n2+6= m5n8

Simplify. Express using exponents.

(7x2y4) (3x4y6)

x2+4 • y4+6= 21x6y10

21

Simplify. Express using exponents.

(9x3y2) (6x5y3)

54x8y5

Multiply:

(-3y3)(4xy5) = -12xy8

Dividing Powers with the same base:

Xm ÷ xn = xm-n

Dividing Powers with the Same Base

xx

xxxxx

x

x

2

53x

Simplify. Express using exponents.

2

5

4

4

325 44

44

44444

Simplify. Express using exponents.

0

7

m

m

707 mm

Divide monomials using properties:Group the numbers together and either divide or reduce and then group the like bases together.

3252

5

xxx

x

2 2 7

7 5

4 4 4

5 5 5

x x

x x

Simplify. Express using exponents.

32

55

qp

qp

233525 qpqp

qqqpp

qqqqqppppp

Simplify. Express using exponents.6 4

2 3

8

2

x y

x q

6 2 4 3x y 4

4 14x y

Simplify. Express using exponents.

5

2

5

5

352 55

55555

55

35

1

nn

aa

Definition

1

:

Divide monomials using properties:

101235103

125

2

8

2

8

yxyx

yx

224 yx

Simplify:

8

5

4

12

m

m 33 m

3

3

m

Simplify:

11

8

9

27

m

m

11 81

3m

3

3

m

Simplify:

yx

yx2

43

5

5

3xy

Homework

• CA Math Page 150 (20-60) even