Simplifying Exponents and Roots

The video tutorial explains division by breaking down numbers into their prime factors. It focuses on understanding cube roots by identifying what number multiplied by itself three times results in a given number. The tutorial demonstrates how to simplify expressions using the rules of exponents, emphasizing the importance of matching the power of variables with the index. The final part of the video shows the complete simplification of a radical expression, resulting in a concise answer.

What is the first step in solving a division problem according to the video?

• Breaking down the problem

• Memorizing multiplication tables

• Guessing the answer

• Using a calculator

How can the number 64 be expressed to simplify division?

• As a fraction

• As a difference of squares

• As a sum of two numbers

• As a product of its prime factors

What does the cube root of a number represent?

• A number added to itself three times

• A number multiplied by itself twice

• A number divided by three

• A number multiplied by itself three times

How do you determine the number of prime factors to group together?

• By the size of the number

• By the index of the root

• By the number of digits in the number

• By the number of factors

What is the rule for multiplying exponents?

• Divide the powers

• Add the powers

• Subtract the powers

• Multiply the powers

How can x to the ninth power be rewritten to simplify cube roots?

• x to the sixth times x cubed

• x cubed times x cubed times x cubed

• x to the fourth times x to the fifth

• x squared times x to the seventh

What happens to the terms when simplifying complex expressions?

• They are divided

• They cancel out

• They are multiplied

• They are added together

What is the final simplified expression in the video?

• 5x squared y

• 4x y squared

• 3x cubed y

• 2x squared y