1. Page 370 – Laws of Exponents Multiplying Monomials
Objectives
Define exponents and powers.
Find products of powers.
Simplify products of monomials.

2. Glossary Terms base of a power coefficient exponent monomial
8.1 Laws of Exponents: Multiplying Monomials
Glossary Terms
base of a power
coefficient
exponent
monomial
Product-of-Powers Property

3. 4 Base and Exponent exponent 3
The exponent tells us how many times the base
is used as a factor.
base

4. Rules and Properties Exponents xm = x  x  x  . . .  x m factors
For all real numbers x and all positive integers m, when m = 1, xm = x1 = x.

5. Evaluate 28 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 = 256 53 = 5 · 5 · 5 = 125
34 =
3 · 3 · 3 · 3 = 81
61 = 6

6. 8.1 Laws of Exponents: Multiplying Monomials
Rules and Properties
Product-of-Powers Property
For all nonzero real numbers x and all integers m and n,
xm  xn = xm+n
When you multiply numbers with the same base, add the exponents.

7. Simplify 23 · 24 = 2 · 2 · 2 · 2 · 2 · 2 · 2 = 27 = 128 8 · 8³ = 8
· 8 · 8 · 8 =
84 =
4096
y2 · y5 =
y2 + 5 = y7
5m · 5p =
5m + p

8. Suppose that a colony of bacteria doubles in size every hour
Suppose that a colony of bacteria doubles in size every hour. If the colony contains 1000 bacteria at noon, how many bacteria will the colony contain at 3 p.m. and 5 p.m. of the same day?
Between noon and 3 p.m. there are 3 hours so there will
be 1000 · 2³, or 8000 bacteria. The 2 stands for the doubling
and the 3 stands for 3 hours.
At 5 p.m., 2 hours later, the bacteria will double 2 more times.
There will be (1000 · 2³) · 2², or 1000 · , or 1000 · 25,
32,000 bacteria in the colony.

9. Rules and Properties Definition of Monomial
8.1 Laws of Exponents: Multiplying Monomials
Rules and Properties
Definition of Monomial
monomial: a constant, variable, or a product of a constant and one or more variables
Coefficient – the number that goes with the variable

10. To multiply monomials
Remove the parentheses and use the commutative and associative properties to rearrange the terms. Group the constants together, and then group like terms together.
Simplify by using the Product-of-Powers Property when appropriate.

11. Simplify (5t)(-30t²) = 5 · (-30) · t · t² = -150t³
(-4a²b)(-ac²)(3b²c²) =
-4 · (-1) · 3 · a² ·a · b · b² · c² · c² =
12a³b³c4
(3m²)(60mp²) =
3 · 60 · m² · m · p² =
180m³p²
(8xz)(-10y)(-2yz²) =
8 · (-10) · (-2) · x · y · y ·z · z² =
160xy²z³

12. Key Skills Simplify the product of monomials containing exponents.
8.1 Laws of Exponents: Multiplying Monomials
Key Skills
Simplify the product of monomials containing exponents.
Simplify (5c2d3)(7cd5)
Group terms with the same base.
Multiply the constants.
= 35
 c2  c  d3  d5
Use the Product-of-Powers Property.
= 35  c2 + 1  d3 + 5
Simplify
= 35c3d8
TOC

13. The volume of a right rectangular prism can be found by using the formula V = lwh. Suppose a prism has a length of 2xy, a width of 3xy, and a height of 6xyz. Find the volume.
V = lwh
= (2xy)(3xy)(6xyz)
= 2 · 3 · 6 · x · x · x · y · y · y · z
= 36x³y³z

14. Assignment
Page 374 – 376
# 10 – 50 even, 52 – 55, 61 – 64,