8.1 MONOMIAL
Multiplying Monomials and Raising Monomials to Powers
VOCABULARY
Let's start with what we know...
Constant – a number by itself
Coefficient – a number used to multiply a variable (in front of the variable or
variable combinations)
Term – a number, variable, or combination of
numbers and variables.
VOCABULARY
TERMS ARE MONOMIALS!!!
Monomials – a number, a variable, or a product of a number
and one or more variables
EXAMPLES:
Base – In an expression of the form xn, the base is x
Exponent – In an expression of the form xn, the exponent is n
x
3
x
3
EXPONENTS AND FORMS
What does this mean?
That's three 2's all multiplied together!
Exponential form
Expanded form
In Algebra, we work with variables like x.
What if there is a coefficient?
WRITING IN EXPONENTIAL FORM
Rewrite the following expressions using exponents:
x x x x y y
a a a b b b b c c d e e
WRITING IN EXPANDED FORM...
Rewrite the following expressions WITHOUT using exponents:
LET'S LOOK AT OPERATIONS...
Can we add these?
Can we multiply them?
Write out what each one means and see what happens...
Example 1:
Example 2:
PRODUCT OF POWERS RULE
Try These:
WHEN CAN'T I USE THIS?
This is addition--not multiplication-and they are NOT like terms!
The bases don't match!
There is nothing we can do with either of these!
MULTIPLYING MONOMIALS WITH
COEFFICIENTS
Multiply the coefficients but still add the powers.
Try These:
MULTIPLYING MONOMIALS WITH DIFFERENT
VARIABLES
Only add powers of like variables.
Example 3:
You Try:
MULTIPLYING MONOMIALS WITH DIFFERENT
VARIABLES
Try These:
POWER TO A POWER RULE
Simplify the following:
Step 1:
Write out the expression in expanded form.
Step 2:
Simplify, writing as a power.
Example 4:
POWER TO A POWER RULE
Try These:
POWER TO A POWER WITH COEFFICIENT
Raise the coefficient to the power, but still multiply the
variable powers.
Try These:
POWER TO A POWER WITH MORE THAN ONE
VARIABLE
Raise each variable to the outside power using the
power to a power rule.
(ab)m = am bm
Example 5:
You Try:
POWER TO A POWER WITH MORE THAN ONE
VARIABLE
Example 6:
POWER TO A POWER WITH MORE THAN ONE
VARIABLE
Try These: