Power of a Product and Exponents

The video tutorial explains how to find the power of a product by applying the power to each factor in a monomial. It provides three examples to illustrate the process, showing how to solve expressions by multiplying the power with each exponent. The tutorial concludes with a summary of the method for raising a product to a power.

What is the first step in finding the power of a product?

• Apply the power to each factor in the monomial.

• Multiply the power by each factor.

• Divide the power by the number of factors.

• Add the exponents of all factors.

In the expression (2xy^4)^2, what is the result of applying the power to the factor '2'?

• 2

• 4

• 8

• 16

How do you calculate the new exponent for 'y' in the expression (2xy^4)^2?

• Divide 4 by 2

• Add 4 and 2

• Multiply 4 by 2

• Subtract 2 from 4

What is the final expression for (2xy^4)^2?

• 4x^2y^8

• 2x^2y^8

• 4x^2y^4

• 2x^2y^4

In the expression (x^2y^3r^4), what is the new exponent for 'x' after applying the power?

• 4

• 6

• 8

• 10

What is the new exponent for 'y' in the expression (x^2y^3r^4)?

• 6

• 12

• 15

• 9

What is the final expression for (x^2y^3r^4) after applying the power?

• x^8y^6r^8

• x^8y^12r^4

• x^8y^9r^12

• x^8y^12r^16

What is the result of applying the power to the factor 'r' in the expression (x^2y^3r^4)?

• r^8

• r^16

• r^12

• r^4

What is the new exponent for 'r' in the expression (x^2y^3r^4)?

• 8

• 12

• 16

• 4

In the expression (xyz^8)^2, what is the new exponent for 'z'?

• 16

• 12

• 8

• 20