1. 7-1 Multiplying Monomials
Algebra Glencoe McGraw-Hill Linda Stamper

2. A monomial is a number, a variable, or a product of a number and one or more variables in which there are
no variables in a denominator,
no variables under a radical sign (√), X X
and any exponents on the variables are positive
integers. X
Monomials that are real numbers are called constants.

3. Determine whether each expression is a monomial. Explain.
Yes, it is a real number.
No, it involves addition.
No, it is has a negative power.
Yes, the variables are a product.
No, it is has a variable in the denominator.
No, it involves subtraction.

4. Today’s lesson involves simplifying monomials involving powers
Today’s lesson involves simplifying monomials involving powers. To simplify these expressions you will need to memorize the multiplication properties of exponents.
Recall an expression like 43 is called a power. 43
base 
 exponent
word form: four to the third power
four cubed
factor form: 4 • 4 • 4
simplified form: 64

5. To multiply powers that have the same base, add the exponents.
Simplify.
How can you get this answer without writing the factored form?
To multiply powers that have the same base, add the exponents.
On tonight’s homework, you must show this support work!
PRODUCT OF POWERS PROPERTY

6. Simplify.
Example 1
Example 2
Example 4
Example 3
Example 5
Example 6

7. Simplify.
Example 1
Example 2
Example 4
Example 3

8. No multiplication dots in answer! No multiplication dots in answer!
Simplify.
Example 5
Example 6
No multiplication dots in answer!
No multiplication dots in answer!

9. To find a power of a power, multiply the exponents.
Simplify.
How can you get this answer without writing the factored form?
To find a power of a power, multiply the exponents.
On tonight’s homework, you must show this support work!
POWER OF A POWER PROPERTY

10. Simplify.
Example 7
Example 8
Example 9

11. POWER OF A PRODUCT PROPERTY
To find the power of a product, find the power of each factor and multiply.
Simplify.
The power is given to each factor inside the parentheses!

12. Example 12 Express the area as a monomial.
Simplify.
Example 10
Example 11
Example 12 Express the area as a monomial.
Example 13 Express the volume as a monomial.
4ab
5xyz
4ab
5xyz
5xyz

13. Using More Than One Property to Simplify.
Example 14
Example 15
Example 16

14. POWER OF A PRODUCT PROPERTY
Memorize the Properties of Exponents
PRODUCT OF POWERS PROPERTY
To multiply powers that have the same base, add the exponents.
POWER OF A POWER PROPERTY
To find a power of a power, multiply the exponents.
POWER OF A PRODUCT PROPERTY
To find the power of a product, find the power of each factor and multiply.

15. Homework
7-A2 Pages # 16–24,29,39–45,48.
Algebra rocks!