Derive the laws of exponent (related to multiplication of
Identify what do you call each of the following:
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
𝟐𝟐 · 𝟐𝟑 = 𝟐𝟐+𝟑 = 𝟐𝟓 = 𝟑𝟐
#2: Power of a Power Law: If you are raising a power to an
exponent, you multiply the exponents!
(𝟐𝟐)𝟑 = 𝟐𝟐∙𝟑 = 𝟐𝟔
#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.
∙ 𝒃 𝟑 𝟒
(𝟒𝒂𝟑)𝟐 = 𝟒(𝟏)(𝟐) ∙ 𝒂(𝟑)(𝟐)
To multiply monomials and polynomials, you will
use some of the properties of exponents that you
1. Multiplying Monomial by a Monomial
To multiply a monomial with another monomial, multiply the
numerical coefficients by applying basic laws of exponent.
B. (-3mn2) (9m2n)
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
12p2q – 6pq2
x y x y
( ) ( )
xy x y 2
3x3y2 + 4x4y3
It’s Your turn…
b. 2(4x2 + x)
c. 5r2s2(r – 3s)
d. 3a(2a + 4ab)
Let’s Sum It Up!
What are the different Laws of exponent for
How do we multiply Polynomials?