Use prime factorization to simplify the fourth root of a radical expression

The video tutorial demonstrates how to simplify the 4th root of 81 * X^16 using two methods. It begins by explaining the property of roots and then factorizes 81 to find its 4th root. The tutorial continues by simplifying X^16 using exponent rules, ultimately arriving at the simplified expression X^4. The video concludes with a summary of the steps taken to achieve the final result.

What property of roots allows us to separate the 4th root of a product into the product of 4th roots?

• The associative property

• The distributive property

• The property of roots

• The commutative property

What is the prime factorization of 81?

• 4 * 4 * 4 * 4

• 5 * 5 * 5 * 5

• 3 * 3 * 3 * 3

• 2 * 2 * 2 * 2

What is the 4th root of 81?

• 5

• 4

• 3

• 2

How can X to the 16th be rewritten to simplify the 4th root?

• As X to the 8th

• As X to the 1st

• As X to the 4th

• As X to the 2nd

What is the simplified form of the 4th root of X to the 16th?

• X to the 2nd

• X to the 3rd

• X to the 4th

• X to the 5th