Exponents and Radical Expressions

The video tutorial explains how to simplify a complex expression by breaking it into parts. It covers simplifying the cube root of 8 squared, 15 raised to the power of 3/2, and 135 raised to the power of 1/2. Each part is simplified using mathematical properties such as perfect cubes, rational exponents, and prime factorization. Finally, the simplified parts are combined to simplify the entire fraction, resulting in a final answer of 20.

What is the first step in simplifying the given expression?

• Simplify the entire expression at once

• Break the expression into parts and simplify each part

• Use a calculator to find the answer

• Guess the answer

What is the cube root of 8?

• 1

• 2

• 4

• 3

How can 8 be expressed as a power of 2?

• 2^2

• 2^3

• 2^4

• 2^5

What is the radical form of 15 raised to the power of three halves?

• Cube root of 15 squared

• Square root of 15 cubed

• 15 to the power of 3

• 15 to the power of 2

What is the perfect square factor of 15 cubed?

• 225

• 45

• 30

• 15

What is the prime factorization of 135?

• 3 * 3 * 3 * 5

• 2 * 2 * 3 * 5

• 3 * 5 * 5

• 2 * 3 * 3 * 5

What is the perfect square factor of 135?

• 5

• 9

• 15

• 25

What is the simplified form of the cube root of 8 squared?

• 5

• 4

• 3

• 2

What is the simplified form of 15 raised to the power of three halves?

• 15 * sqrt(15)

• 15

• 15 * 3

• 15 * 15

What is the final simplified result of the expression?

• 15

• 25

• 20

• 10