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, emphasizing that everything inside parentheses gets the exponent outside. Examples include handling exponents inside parentheses and complex cases with multiple variables.

What two mathematical rules combine to form the Power of a Product Rule?

• Power and Product Rules

• Division and Multiplication Rules

• Addition and Subtraction Rules

• Exponent and Root Rules

If you have (xy)^2, what is the result after applying the Power of a Product Rule?

• x^2y^2

• 2xy

• x^2y

• x^2 + y^2

How do you simplify (2x)^3 using the Power of a Product Rule?

• 6x^3

• 2x^3

• 2^3x^3

• 8x^3

When you have an exponent inside the parentheses, what operation do you perform with the outer exponent?

• Subtract the exponents

• Add the exponents

• Divide the exponents

• Multiply the exponents

What is the result of (2x^2)^5 after applying the Power of a Product Rule?

• 2^5x^7

• 2^5x^10

• 10x^10

• 32x^5

In the expression (-5xy^3z)^2, why is it important to keep the negative sign in parentheses?

• To make the expression look neat

• To separate it from the variables

• To ensure the negative sign is squared

• To avoid confusion with positive numbers

What is the simplified form of (-5xy^3z)^2?

• -25x^4y^6z^2

• 25x^4y^6z^2

• -25x^2y^6z^2

• 25x^2y^6z^2

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

• Only the denominator gets the exponent

• Both numerator and denominator get the exponent

• Only the numerator gets the exponent

• It doesn't apply to fractions

What is the result of (1/4x^2y)^3 after applying the Power of a Product Rule?

• 1/64x^6y^3

• 1/12x^6y^3

• 1/12x^3y^6

• 1/64x^3y^6

What is the simplified form of (1/4)^3?

• 1/16

• 1/12

• 1/64

• 1/32