Download Multiplying and Dividing Monomials

Warm Up
Write in exponential form.
1. 6 · 6 · 6 · 6 · 6
65
2. 3x · 3x · 3x · 3x
(3x)4
Simplify.
3. 34
81
4. (–3)5
–243
5. (24)5
220
6. (42)0
1
Multiplying and
Dividing Monomials
Section 4.4
California
Standards
AF2.2 Multiply and divide monomials;
extend the process of taking powers and
extracting roots to monomials when the latter
results in a monomial with an integer exponent.
Also covered: AF1.3
Words to Know
A monomial is a number or a product of
numbers and variables with exponents that are
whole numbers.
Monomials
Not
monomials
z
8,
4
8
m-3,4z2.5, 5 + y, w3 , 2x
7x5,
-3a2b3,
n 2,
Multiplying Monomials
3a 4a 
2
5
1. Multiply just the coefficients
first.
2. Add the exponents that have
the same base.
Multiplying Monomials
1. (4x2y3)(5xy5)
20x3y8
1. Multiply just the
coefficients first.
2. Add the exponents that
have the same base.
2. (–3p2r)(6pr3s) –18p3r4s
Try on your own…..
Multiply.
A. (2b2)(7b4)
B. (4n4)(5n3)(p)
C. (–2a4b4)(3ab3c)
14b6
20n7p
–6a5b7c
Dividing Monomials
15m5
3m2
1. Divide just the coefficients
first.
2. Subtract the exponents
that have the same base.
Dividing Monomials
18a2b3
16ab3
9a
8
18x7
6x2
3x5
12m2n3
9mn2
4 mn
3
Raising a monomial to a power…
To raise a monomial to a power, you must first
understand how to find a power of a product. Notice
what happens to the exponents when you find a power
of a product.
(xy)3 = xy ∙ xy ∙ xy = x ∙ x ∙ x ∙ y ∙ y ∙ y = x3y3
Raising a monomial to a
power…
Simplify.
A. (3y)3
27y3
33 ∙ y3
B. (2a2b6)4
24 ∙ (a2)4 ∙ (b6)4
16a8b24
Try on your own….
A. (4a)4
256a4
B. (–3x2y)2
9x4y2
Summary
When multiplying a monomial, remember to
add the exponents.
When dividing monomials, remember to
subtract the exponents.
Lesson Quiz
Multiply.
1. (3g2h3)(–6g7h2)
–18g9h5
2. (12m3)(3mp3) 36m4p3
Divide. Assume that no denominator equals zero.
6b4
6a
3.
3a2b
2a4b3
3y
9x
4.
6x2y
Simplify.
6.(–5y7)3
–125y21
7. (3c2d3)4
81c8d12
8. (3m2n)5
243m10n5
3
x
2
5q
20p
5.
–4p2q
–5p3