8.1 MONOMIALSMultiplying Monomials and Raising Monomials to Powers

VOCABULARYLet's start with what we know...

Constant – a number by itselfCoefficient – 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.

VOCABULARYTERMS 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 xExponent – In an expression of the form xn, the exponent is n

3yz 4x 20x2yw2a2b3

-3

x 3x 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:

a a a b b b b c c d e e

x x x x y y

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!

Multiply the coefficients but still add the powers.

MULTIPLYING MONOMIALS WITH COEFFICIENTS

Try These:

You Try:

Example 3:

MULTIPLYING MONOMIALS WITH DIFFERENT VARIABLESOnly add powers of like variables.

MULTIPLYING MONOMIALS WITH DIFFERENT VARIABLES

Try These:

Simplify the following:

Step 1: Write out the expression in expanded form.

Step 2: Simplify, writing as a power.

POWER TO A POWER RULE

Example 4:

POWER TO A POWER RULE

Try These:

POWER TO A POWER WITH COEFFICIENTRaise the coefficient to the power, but still multiply the variable powers.

Try These:

Example 5:

You Try:

POWER TO A POWER WITH MORE THAN ONE VARIABLERaise each variable to the outside power using

the power to a power rule.(ab)m = am bm

POWER TO A POWER WITH MORE THAN ONE VARIABLE

Example 6:

POWER TO A POWER WITH MORE THAN ONE VARIABLE

Try These: