Exponents and Radicals Practice

The video tutorial explains how to simplify the expression d times 4d to the 1/2 power. It begins by breaking down the expression into its components, showing that 4d to the 1/2 can be expressed as 4 to the 1/2 times d to the 1/2. The tutorial then demonstrates how to simplify 4 to the 1/2 using square roots, resulting in 2. It further explores combining d and d to the 1/2, offering different ways to represent the simplified expression, such as 2 times d to the 3/2 or 2 times d times the square root of d. The video emphasizes that these are all valid simplifications of the original expression.

What is the initial expression that needs to be simplified?

• d times 4d to the 1/2 power

• d times 4 to the 1/2 power

• 4d times d to the 1/2 power

• 4 times d to the 1/2 power

How can 4d to the 1/2 be expressed using exponents?

• 4d to the 1/2

• 4 to the 1/2 times d to the 1/2

• 4 times d to the 1/2

• 4 to the 1/2 times d

What is the principal square root of 4?

• 1

• 2

• 3

• 4

How can you combine d and d to the 1/2?

• d to the 2

• d to the 1

• d to the 1/2

• d to the 3/2

What is the simplified form of 2 times d to the 1 plus 1/2?

• 2 times d cubed

• 2 times d squared

• 2 times d to the 3/2

• 2 times d to the 1/2

What is the result of adding the exponents 1 and 1/2?

• 1

• 1/2

• 3/2

• 2

What is another way to express d to the 1/2?

• d to the 1

• d squared

• Square root of d

• d cubed

Which of the following is a valid simplification of the expression?

• 2 times d times the square root of d

• 2 times d squared

• 2 times d cubed

• 2 times d to the 1/2

What is the exponent form of the expression 2 times d times the square root of d?

• 2 times d squared

• 2 times d to the 3/2

• 2 times d to the 1/2

• 2 times d cubed

Which of the following expressions is equivalent to 2 times d to the 3/2?

• 2 times d squared

• 2 times d times the square root of d

• 2 times d to the 1/2

• 2 times d cubed