Objectives The student will be able to:

1
ObjectivesThe student will be able to
1. multiply monomials. 2. simplify expressions
with monomials.
2
A monomial is a

• 1. number,
• 2. variable, or
• 3. the product of one or more numbers and
  variables.
• Examples
• 5
• y
• 3x2y3

3
Why are the following not monomials? x y

• addition
• division
• 2 - 3a
• subtraction

4
Multiplying Monomials

• When multiplying monomials, you ADD the
  exponents.
• 1) x2 x4
• x24
• x6
• 2) 2a2y3 3a3y4
• 6a5y7

5
Simplify m3(m4)(m)

1. m7
2. m8
3. m12
4. m13

6
Power of a Power

• When you have an exponent with an exponent, you
  multiply those exponents.
• 1) (x2)3
• x2 3
• x6
• 2) (y3)4
• y12

7
Simplify (p2)4

1. p2
2. p4
3. p8
4. p16

8
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

9
Simplify (4r)3

1. 12r3
2. 12r4
3. 64r3
4. 64r4

10
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

11
Simplify (3a2b3)4

1. 12a8b12
2. 81a6b7
3. 81a16b81
4. 81a8b12