Simplifying a radical expression into rational exponents

The video tutorial covers the product rule of radicals, explaining how to break down products of radicands using radicals. It demonstrates converting radicals into rational exponents and simplifying expressions, particularly focusing on simplifying 81 to the one fourth power. The tutorial also explores the power to power rule and provides alternative methods for simplification, ensuring a comprehensive understanding of the concepts.

What does the product rule of radicals allow you to do with a product of radicands?

• Multiply them by a constant

• Convert them into fractions

• Break them into separate radicals

• Combine them into a single radical

How can you express the 4th root of a number using rational exponents?

• Raise the number to the power of 4

• Raise the number to the power of 1/4

• Multiply the number by 4

• Divide the number by 4

What is the rational exponent form of Z to the fifth power under a 4th root?

• Z to the power of 5/4

• Z to the power of 4/5

• Z to the power of 1/5

• Z to the power of 5

Which of the following is a correct simplification of 81 to the 1/4 power?

• 81 to the 1/2 power

• 3 to the 1st power

• 9 to the 1/2 power

• 27 to the 1/3 power

What is the result of applying the power to power rule to 3 to the 4th power raised to the 1/4 power?

• 3 to the 1st power

• 3 to the 2nd power

• 3 to the 1/4 power

• 3 to the 4th power