The document discusses laws of exponents and multiplying polynomials. It defines exponent, base, and power. It describes four laws of exponents for multiplication: 1) the product law, which states that when multiplying powers with the same base you add the exponents, 2) the power of a power law, which states that when raising a power to an exponent you multiply the exponents, 3) the product law of exponents, which states that when multiplying bases powered by the same exponent you multiply the individual factors each powered by the exponent, and 4) the zero law of exponents, which states that any base powered by zero equals one. It then explains how to multiply monomials by applying laws of exponents and how to multiply polynomials using the distribut

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

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

4. 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

5. Try This:
Solutions:

6. #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

7. #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

8. Try This:
Solutions:

9. #4: Zero Law of Exponents: Any base powered by zero
exponent equals one.
𝒂𝟎
= 𝟏
𝟐𝟎
= 𝟏 −𝟐𝟎
= −𝟏
(−𝟐)𝟎
= 𝟏

10. Try This:
Solutions:

11. 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

12. 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

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

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