Fourth Roots and Simplification Techniques

The video tutorial explains how to simplify expressions involving the fourth root. It covers handling negative numbers outside the radical, breaking down powers for simplification, and using the power rule for expressions. The tutorial provides examples to illustrate these concepts and concludes with additional resources for further learning.

What is the main goal when simplifying a fourth root?

• To rewrite it as a square root

• To express it as a number raised to the fourth power

• To find the cube root

• To multiply it by itself four times

Why can't we take the fourth root of a negative number?

• Because it is always positive

• Because it results in a complex number

• Because it equals zero

• Because it is undefined

What is a cortic number?

• A number that can be expressed as a fifth power

• A number that can be expressed as a square

• A number that can be expressed as a cube

• A number that can be expressed as a fourth power

How can 81 be expressed as a fourth power?

• 2^4

• 3^4

• 5^4

• 4^4

What is the result of simplifying -7 times the fourth root of 81?

• 27

• -27

• 21

• -21

What is the fourth root of 64?

• 2

• 4

• 16

• 8

How can you express 8 to the 18th power using the power rule?

• 8^4 * 8^6

• 8^4 * 8^4

• 8^4 * 8^10

• 8^4 * 8^2

What is the fourth root of 16?

• 2

• 4

• 8

• 16

What is the simplified form of 18 times the fourth root of 64?

• 36

• 72

• 18

• 54

What should you do when you have an expression raised to the 16th power?

• Distribute the power across all terms

• Divide it by 4

• Rewrite it as a fourth power

• Multiply it by 16