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

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.

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.

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

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

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

Simplify. Example 1 Example 2 Example 4 Example 3

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!

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

Simplify. Example 7 Example 8 Example 9

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!

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

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

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.

Homework 7-A2 Pages 361-362 # 16–24,29,39–45,48. Algebra rocks!