Cube Roots and Exponents Concepts

The video tutorial explains how to work with cube roots, focusing on simplifying expressions involving cube roots of different and same bases. It demonstrates the process of combining cube roots under a single radical and simplifying them using both radical and exponential forms. The tutorial provides examples, such as the cube root of 7 times the cube root of 2, and the cube root of 9 times the cube root of 9, to illustrate these concepts.

What is the cube root of 7 times the cube root of 2 simplified under a single radical?

• Cube root of 9

• Cube root of 14

• Cube root of 49

• Cube root of 21

Why can't the cube root of 14 be simplified further?

• Because 14 is a perfect cube

• Because 14 breaks down to 2 times 7, which are both primes

• Because 14 is already in its simplest form

• Because 14 is a prime number

What is the result of multiplying the cube root of 9 by itself?

• Cube root of 18

• Cube root of 27

• Cube root of 36

• Cube root of 81

How can the cube root of 81 be simplified?

• Cube root of 9

• 9 cube root of 9

• Cube root of 27

• 3 cube root of 3

What is the cube root of 81 in terms of its prime factors?

• 3 times 3 times 3

• 3 times 3 times 3 times 3

• 3 times 9

• 9 times 9

What is the cube root of 81 when expressed as a product of its prime factors?

• 9 times 9

• 3 times 3 times 3 times 3

• 3 times 3

• 3 times 3 times 3

What does 9 to the 2/3 represent in terms of cube roots?

• The square root of 9 cubed

• The cube of 9

• The cube root of 9 squared

• The square of 9

How can you express 9 to the 2/3 using radicals?

• Cube root of 9

• Square root of 81

• Square root of 9

• Cube root of 81

Which of the following is a rational way to express 9 to the 2/3?

• Cube root of 81

• Square root of 9 cubed

• Square root of 81

• Cube root of 9 squared