Exponent and Factorization Concepts

The video tutorial explains how to write expressions in simplified radical form. It begins with an introduction to the concept, followed by a demonstration of breaking down numbers using a factor tree. The tutorial then addresses handling variables with exponents, extracting terms from the expression, and concludes with writing the final simplified expression.

What is the main goal when simplifying a radical expression?

• To eliminate all variables

• To increase the exponent inside the radical

• To make the exponent inside a radical a multiple of the number outside

• To convert the expression into a fraction

What is the significance of the number 5 in this context?

• It is the number of steps

• It is the number outside the radical

• It is the number of variables

• It is the number of terms

What is the first step in simplifying the number 96?

• Use a factor tree

• Subtract 10

• Multiply by 2

• Divide by 3

What is the prime factorization of 96?

• 3 x 2^5

• 2 x 3^5

• 5 x 2^3

• 3 x 5^2

What is the purpose of using a factor tree?

• To convert numbers into fractions

• To add numbers

• To multiply numbers

• To break down a number into its prime factors

What is the result of dividing 96 by 2 repeatedly?

• A factor tree showing 3 x 2^5

• A factor tree showing 2 x 3^5

• A factor tree showing 3 x 5^2

• A factor tree showing 5 x 2^3

How can the expression be rewritten using the prime factorization of 96?

• As 2 x 3^3

• As 5 x 3^2

• As 3 x 2^5

• As 3 x 5^3

Why is Z to the 14th power broken down in the expression?

• To make it a multiple of 5

• To convert it into a fraction

• To increase its value

• To eliminate Z

What is the highest multiple of 5 that can be used for Z?

• Z^10

• Z^5

• Z^15

• Z^20

What happens to the exponent of Z when it is broken down?

• It is halved

• It is eliminated

• It is doubled

• It is split into Z^10 and Z^4