Understanding the Product of Monomials

The video tutorial explains how to multiply monomials by focusing on two examples. It covers the multiplication of coefficients and variables, using the commutative property to rearrange terms for easier calculation. The first example involves multiplying monomials with a single variable, while the second example includes multiple variables and negative coefficients. The tutorial emphasizes the importance of adding exponents when the bases are the same, resulting in a final product for each example.

What is the first step in finding the product of monomials?

• Divide the variables

• Multiply the coefficients

• Add the coefficients

• Subtract the exponents

Which property allows us to change the order of multiplication?

• Associative Property

• Commutative Property

• Identity Property

• Distributive Property

In the first example, what is the product of the coefficients 8, 4, and 6?

• 192

• 128

• 256

• 64

How do you determine the total exponent for x in the first example?

• Add the exponents

• Multiply the exponents

• Divide the exponents

• Subtract the exponents

What is the final product of the first example?

• 192x^12

• 192x^10

• 192x^17

• 192x^15

In the second example, what is the exponent of x in the term 2xy^3?

• 1

• 3

• 4

• 2

What is the product of the coefficients 2, -3, and 4 in the second example?

• -24

• 24

• -12

• 12

How do you calculate the total exponent for y in the second example?

• Multiply the exponents

• Add the exponents

• Subtract the exponents

• Divide the exponents

What is the final product of the second example?

• -24x^8y^8

• -24x^7y^7

• -24x^5y^5

• -24x^6y^6

What is the importance of recognizing the exponent on variables in the second example?

• To add the coefficients correctly

• To multiply the variables correctly

• To divide the variables correctly

• To add the exponents correctly