Understanding Radical Expressions and Exponent Properties

The video tutorial explains how to express 'd times 4d to the fourth to the 1/2 power' as a radical expression. It begins by defining the 1/2 power as the principal root and applies this to simplify the expression. The tutorial demonstrates the simplification process, showing that the expression becomes '2 times d to the third power'. An alternative method using exponent properties is also presented, reinforcing the concept that raising a product to an exponent is equivalent to raising each factor to the exponent individually.

What is the expression d times 4d to the fourth to the 1/2 power equivalent to in radical form?

• d times the square root of 4d to the fourth

• d times 4d to the fourth

• d times the cube root of 4d to the fourth

• d times 4d squared

What does raising a number to the 1/2 power represent?

• Squaring the number

• Multiplying the number by 2

• Taking the principal root of the number

• Dividing the number by 2

What is the principal root of 4?

• 1

• 2

• 3

• 4

How can the principal root of d to the fourth be expressed?

• d squared

• d

• d cubed

• d to the fourth

Why is there no need for an absolute value when simplifying d squared?

• Because d squared is zero

• Because d squared is always negative

• Because d squared is always positive

• Because d squared is undefined

What is the simplified form of d times 2 times d squared?

• 2d cubed

• 2d

• 2d squared

• 2d to the fourth

What exponent property is used to simplify 4d to the fourth to the 1/2 power?

• Negative exponent

• Quotient of powers

• Power of a power

• Product of powers

What is the result of raising 4 to the 1/2 power?

• 4

• 1

• 2

• 3

What is the final simplified form of the expression?

• 2d cubed

• d cubed

• d squared

• 2d squared

What is the product of the powers when simplifying d to the fourth to the 1/2 power?

• 4

• 3

• 2

• 1