Cube Roots and Exponents

The video tutorial explains how to find the cube root of negative 512. It begins by introducing the concept of cube roots and suggests using prime factorization to solve the problem. The tutorial then breaks down the factorization of 512 into its prime components, emphasizing the role of negative numbers in cube roots. By identifying groups of factors, the tutorial demonstrates that the cube root of 512 is 8, and thus the cube root of negative 512 is negative 8. The video concludes with a verification of the result.

What is the cube root of negative 512?

• 8

• -8

• -512

• 512

If a number raised to the third power equals negative 512, what is the number?

• -8

• 8

• 64

• -64

What is the cube root of negative 1?

• 2

• 0

• 1

• -1

How many times does the factor 2 appear in the prime factorization of 512?

• 9

• 8

• 7

• 6

What is 2 raised to the ninth power?

• 64

• 512

• 128

• 256

How many groups of three 2s can be formed from the prime factorization of 512?

• 4

• 2

• 3

• 1

What is the result of 2 times 2 times 2?

• 2

• 8

• 4

• 6

What is the cube root of 512 expressed as a product of identical factors?

• 8 times 8 times 8

• 4 times 4 times 4

• 2 times 2 times 2

• 16 times 16 times 16

What is the final answer for the cube root of negative 512?

• 64

• -8

• 8

• -64

What is the result of multiplying negative 8 by itself three times?

• -64

• 512

• -512

• 64