The video tutorial explains the process of simplifying expressions using the product rule and square numbers. It begins with a discussion on the complexity of prime factorization of 16 and then introduces the product rule to simplify expressions. The instructor breaks down the expression 16 and X^8 into squares and demonstrates how to calculate their square roots to arrive at the final answer, X^4.

Why does the teacher prefer not to perform the prime factorization of 16?

• It involves too many repetitions of the same number.

• It involves too many different numbers.

• It cannot be expressed as a product of prime numbers.

• It is too complex to solve.

What mathematical rule does the teacher use to simplify expressions involving square numbers?

• Product Rule

• Difference Rule

• Quotient Rule

• Sum Rule

How does the teacher rewrite the number 16 to simplify taking its square root?

• As 4^2

• As 8^2

• As 2^4

• As 16^1

How is X to the 8th power rewritten to facilitate taking the square root?

• As X^3 * X^3 * X^2

• As X^8

• As X^4 * X^4

• As X^2 * X^2 * X^2 * X^2

What is the final simplified expression after taking the square roots?

• 4X^5

• 4X^4

• 4X^3

• 4X^2