Transcript Multiplying Monomials - Pascack Valley Regional High

Objectives
The student will be able to:
1. multiply monomials.
2. simplify expressions with monomials.
SOL: A.10
Designed by Skip Tyler, Varina High School
A monomial is a
1. number,
2. variable, or
3. a product of one or more
numbers and variables.
Examples:
5
y
3x2y3
Why are the following not
monomials?
x+y
addition
x
y
division
2 - 3a
subtraction
Multiplying Monomials
When multiplying monomials, you
ADD the exponents.
1) x3 • x8
x3+8
x11
2) 2a2y3 • 3a3y4
6a5y7
Simplify
1.
2.
3.
4.
m7
m8
12
m
13
m
3
4
m (m )(m)
Power of a Power
When you have an exponent raised to
another exponent, you multiply those
exponents.
1) (x4)7
x4• 7
x28
2) (y3)4
y12
Simplify
1.
2.
3.
4.
p2
p4
8
p
16
p
2
4
(p )
Power of a Product
When you have a power outside of the
parentheses, everything in the
parentheses is raised to that power.
1) (2a)3
23a3
8a3
2) (3x)2
9x2
Simplify
1.
2.
3.
4.
12r3
12r4
3
64r
4
64r
3
(4r)
Power of a Monomial
This is a combination of all of the other
rules.
1) (x3y2)4
x3• 4 y2• 4
x12 y8
2) (4x4y3)3
64x12y9
Simplify
1.
2.
3.
4.
12a8b12
81a6b7
16
81
81a b
8
12
81a b
2
3
4
(3a b )