1.
 Derive the laws of exponent (related to multiplication of
polynomials)
 Multiply Polynomials

2.
Identify what do you call each of the following:
exponent
base
Power

3.
Laws of Exponent (for Multiplication)
#1: The Product Law: If you are multiplying powers with
the same base, KEEP the BASE & ADD the
EXPONENTS! So, I get
it! When
you
multiply
powers,
you add
the
exponents!
𝒂𝟐
· 𝒂𝟑
= 𝒂𝟐+𝟑
= 𝒂𝟓
𝟐𝟐 · 𝟐𝟑 = 𝟐𝟐+𝟑 = 𝟐𝟓 = 𝟑𝟐

4.
Try This:
Solutions:

5.
#2: Power of a Power Law: If you are raising a power to an
exponent, you multiply the exponents!
(𝒂𝒎
)𝒏
= 𝒂𝒎𝒏
(𝟐𝟐)𝟑 = 𝟐𝟐∙𝟑 = 𝟐𝟔

6.
#3: Product Law of Exponents: If the product of the bases is
powered by the same exponent, then the result is a
multiplication of individual factors of the product, each
powered by the given exponent.
(𝒂𝒎
∙ 𝒃𝒏
)𝒙
= 𝒂𝒎𝒙
𝒃𝒏𝒙
(𝒂𝟐
∙ 𝒃𝟑
)𝟒
= 𝒂(𝟐)(𝟒)
∙ 𝒃 𝟑 𝟒
= 𝑎8
𝑏12
(𝟒𝒂𝟑)𝟐 = 𝟒(𝟏)(𝟐) ∙ 𝒂(𝟑)(𝟐)
= 𝟒𝟐
𝒂𝟔
= 𝟏𝟔𝒂𝟔

7.
Try This:
Solutions:

8.
#4: Zero Law of Exponents: Any base powered by zero
exponent equals one.
𝒂𝟎
= 𝟏
𝟐𝟎
= 𝟏 −𝟐𝟎
= −𝟏
(−𝟐)𝟎
= 𝟏

9.
Try This:
Solutions:

10.
Multiplying Polynomials
 To multiply monomials and polynomials, you will
use some of the properties of exponents that you
learned earlier
1. Multiplying Monomial by a Monomial
To multiply a monomial with another monomial, multiply the
numerical coefficients by applying basic laws of exponent.
A. (6y3)(3y5)
(6y3)(3y5)
18y8
B. (-3mn2) (9m2n)
(-3mn2)(9m2n)
-27m3n3

11.
B.
Multiplying Polynomials
To multiply a polynomial by a monomial, use
the Distributive Property.
2. Multiplying Monomial by a Polynomial
A. 6pq(2p – q)
(6pq)(2p – q) Distribute 6pq
(6pq)2p + (6pq)(–q)
Group like bases
together.
12p2q – 6pq2
x y
( )
+
2
2
6
1
2
xy
y
x 8
2
x y x y
( ) ( )



+
2 2
1
6
2
8
xy x y 2
2



1
2






3x3y2 + 4x4y3

12.
It’s Your turn…
b. 2(4x2 + x)
c. 5r2s2(r – 3s)
d. 3a(2a + 4ab)
a. (2t)(5t3)

13.
Let’s Sum It Up!
What are the different Laws of exponent for
Multiplication?
How do we multiply Polynomials?