Power of a Product Property

This lesson explains how to raise a product to a power using examples. It demonstrates the process of expanding expressions and applying the commutative and associative properties of multiplication. The lesson introduces the power of a product property, which simplifies the process by allowing the exponent to be distributed to each factor within the product. The video concludes with a practical application of this rule to simplify expressions.

What does the exponent indicate when raising a product to a power?

• The number of times the product is subtracted

• The number of times the product is divided

• The number of times the product is multiplied

• The number of times the product is added

How can the expression (X^3 * Y^4)^2 be simplified using properties of exponents?

• X^6 * Y^8

• X^5 * Y^6

• X^9 * Y^12

• X^3 * Y^4

What is the power of a product property?

• A property that allows multiplication of exponents

• A property that allows addition of exponents

• A property that allows subtraction of exponents

• A property that allows division of exponents

How do you determine the power of a factor inside the parenthesis when using the power of a product property?

• By adding the exponents

• By subtracting the exponents

• By multiplying the exponents

• By dividing the exponents

If X * Y^2 is raised to the power of 5, what is the simplified expression?

• X^5 * Y^2

• X^2 * Y^5

• X^10 * Y^5

• X^5 * Y^10