Apply power to product and power to quotient rule with rational powers

The video tutorial explains how to apply power product and quotient rules to expressions, focusing on simplifying terms by using radicals. It demonstrates the process of simplifying fractions and finding common factors to achieve a final simplified expression. The tutorial concludes with the final answer, emphasizing the importance of understanding these mathematical concepts.

What is the first step in applying the power and quotient rules to an expression?

• Apply the exponent to each term individually.

• Add the exponents of all terms.

• Subtract the exponents of the terms.

• Divide the exponents by the number of terms.

When an exponent is raised to another power, what operation is performed on the powers?

• They are added together.

• They are divided.

• They are subtracted.

• They are multiplied.

What is the simplified form of sqrt(12) / sqrt(75)?

• sqrt(1/2)

• sqrt(12/75)

• sqrt(4/25)

• sqrt(3/5)

What common factor is used to simplify the fraction 12/75?

• 2

• 4

• 3

• 5

What is the final simplified expression of the given problem?

• X^4 / 5Y^5

• X^4 / Y^5

• 2X^4 / 5Y^5

• 4X^4 / 25Y^5