Monomials and Exponent Rules

The video tutorial covers dividing monomials, focusing on two main rules: the quotient of powers and the power of a quotient. The teacher explains each rule with examples, demonstrating how to apply them to simplify expressions. The tutorial emphasizes understanding the subtraction of exponents and distributing exponents across terms in a fraction. Through examples, students learn to handle multiple variables and complex expressions, reinforcing the rules and their applications.

What is a monomial?

• A polynomial with two terms

• A single term expression

• An equation with multiple variables

• A fraction with different bases

When dividing monomials with the same base, what operation is performed on the exponents?

• Add the exponents

• Multiply the exponents

• Divide the exponents

• Subtract the exponents

In the quotient of powers rule, which exponent is subtracted from which?

• Base from exponent

• Exponent from base

• Numerator from denominator

• Denominator from numerator

What happens to the exponent in the power of a quotient rule?

• It is subtracted from the base

• It is divided by the base

• It is distributed to both the numerator and denominator

• It is added to the base

In the power of a quotient rule, what is the result when the exponent is applied to both the numerator and denominator?

• Each term is raised to the power of the exponent

• The base remains unchanged

• The exponent is added to the base

• The terms are multiplied by the exponent

In the example of applying the quotient of powers rule, what is the result of a^4 / a^1?

• a^2

• a^1

• a^5

• a^3

What is the simplified form of b^7 / b^2 using the quotient of powers rule?

• b^9

• b^5

• b^3

• b^1

In the complex example, what is the result of distributing the exponent 3 to the term 2?

• 12

• 9

• 8

• 6

What is the result of raising b^2 to the power of 3?

• b^5

• b^9

• b^6

• b^8

What is the final simplified form of the expression a^8 b^9 / 27?

• a^9 b^9 / 27

• a^8 b^9 / 27

• a^8 b^8 / 27

• a^9 b^8 / 27