Power of a Product Rule

Mrs. Mallet explains the power of a product rule, which combines the power rule and product rule. She demonstrates how to apply this rule to variables, numbers, and fractions, ensuring that each element inside parentheses receives the exponent outside. The video includes examples with variables, numbers, and fractions, and addresses handling exponents inside parentheses.

What is the Power of a Product Rule a combination of?

• The difference rule and the power rule

• The power rule and the product rule

• The power rule and the quotient rule

• The sum rule and the product rule

When applying the Power of a Product Rule, what happens to the exponent outside the parentheses?

• It is added to each term inside the parentheses

• It is subtracted from each term inside the parentheses

• It is multiplied by each term inside the parentheses

• It is distributed to each term inside the parentheses

What is the result of applying the Power of a Product Rule to (x * y)^2?

• x * y^2

• x^2 * y

• x^2 * y^2

• x^3 * y^3

If you have (2x)^3, what is the simplified form using the Power of a Product Rule?

• 2 * x^3

• 2^3 * x^3

• 2^3 * x

• 2 * x

How do you handle an exponent inside the parentheses when applying the Power of a Product Rule?

• Divide the exponents

• Add the exponents together

• Multiply the exponents

• Subtract the exponents

What is the simplified form of (2x^2)^5 using the Power of a Product Rule?

• 2^5 * x^5

• 2 * x^5

• 2 * x^10

• 2^5 * x^10

In the example with -5, X, Y, and Z, why is it important to keep the negative sign in parentheses?

• To separate it from the variables

• To make the calculation easier

• To avoid confusion with positive numbers

• To ensure the negative sign is applied to the exponent

In the example with -5, X, Y, and Z, what is the final simplified form?

• -25x^2y^3z

• 25x^2y^3z

• -25x^4y^6z^2

• 25x^4y^6z^2

How does the Power of a Product Rule apply to fractions?

• The exponent is only applied to the numerator

• The exponent is only applied to the denominator

• The exponent is ignored for fractions

• The exponent is applied to both the numerator and the denominator

What is the simplified form of (1/4 * x^2 * y)^3 using the Power of a Product Rule?

• 1/4 * x^3 * y^2

• 1/64 * x^3 * y^2

• 1/64 * x^6 * y^3

• 1/4 * x^6 * y^3