Exponent Rules and Applications

The video tutorial explains the power to product and power to quotient rules, emphasizing that exponents distribute over multiplication and division but not over addition or subtraction. Common mistakes are highlighted, such as incorrectly distributing exponents over addition. The tutorial provides a step-by-step example to demonstrate the correct application of these rules, ensuring students understand the difference between operations involving exponents and those involving simple numbers.

What is the main idea behind the power to product and power to quotient rules?

• They allow distribution of power over all operations.

• They allow distribution of power over subtraction.

• They allow distribution of power over multiplication and division.

• They allow distribution of power over addition.

Which operation does NOT allow the distribution of an exponent?

• None of the above

• Multiplication

• Division

• Addition

Why can't exponents be distributed over addition?

• Because addition changes the base.

• Because it results in a different mathematical operation.

• Because it is only applicable to multiplication and division.

• Because it simplifies the expression incorrectly.

What is the correct interpretation of (x + 2)^2?

• x^2 + 2x + 2

• x^2 + 4

• x^2 + 4x + 4

• x^2 + 2

When can the distributive property be applied?

• With numbers over addition

• With exponents over addition

• With numbers over division

• With exponents over subtraction

What is the result of 2^3?

• 9

• 12

• 8

• 6

How do you apply the power to product rule to y^4 raised to the 3rd power?

• y^3

• y^12

• y^7

• y^1

What is the result of (2x)^3?

• 6x^3

• 8x

• 8x^3

• 2x^3

Which of the following is a correct application of the power to quotient rule?

• (x/y)^2 = x^2y^2

• (x/y)^2 = x^2/y^2

• (x/y)^2 = x/y^2

• (x/y)^2 = x^2/y

What is the result of (3y)^2?

• 3y^2

• 9y^2

• 6y^2

• 9y