Multiplying Monomials: Key Concepts and Techniques

The video tutorial covers the multiplication of monomials, including those with and without coefficients. It explains the process of expanding terms, counting exponents, and applying rules for rational and zero exponents. Examples are provided to illustrate these concepts, and the use of calculators for handling rational exponents is demonstrated.

What is the result of multiplying the coefficients 5 and 2 in the expression 5x^4 * 2x^8?

• 10

• 12

• 14

• 7

How many total x's are there in the expression 5x^4 * 2x^8?

• 13

• 12

• 11

• 10

In the expression a * a^4 * a^8, what is the total number of a's?

• 14

• 10

• 12

• 13

What is the product of the coefficients 4, 10, and 2 in the expression 4a^2b^3 * 10a^4b^6 * 2?

• 90

• 80

• 70

• 60

How many total b's are there in the expression 4a^2b^3 * 10a^4b^6 * 2?

• 7

• 8

• 9

• 10

What is the result of adding the exponents 1/2 and 3/4 in the expression 4x^(1/2) * 5x^(3/4)?

• 1

• 7/4

• 5/4

• 3/2

What is the product of the coefficients 8 and 4 in the expression 8x^(1/2) * 4x^(3/4)?

• 28

• 24

• 36

• 32

What is the value of any number raised to the zero power?

• Undefined

• The number itself

• 1

• 0

In the expression -2z^0 * -3z, what is the simplified result?

• -6

• 6

• -3

• 3

What happens to a variable when it is raised to the zero power?

• It becomes zero

• It remains the same

• It is removed from the expression

• It becomes one