Question

Which of the following options represents 16 to the power of 3/2 written in radical form?

A) √16^3/2
B) √(16^3)/2
C) (16^3)^(1/2)
D) (16^(3/2))^2

Answer 1

The correct option that represents 16 to the power of 3/2 in radical form is option C: (16^3)^(1/2), which corresponds to the square root of 16 raised to the third power.

Step-by-step explanation:

The student asked which option represents 16 to the power of 3/2 written in radical form. To express a power as a radical, you can use the fact that an exponent of ½ corresponds to a square root. According to this, 16 to the power of 3/2 can be written as the square root of 16 raised to the power of 3, which is (16^(3/2))^1. However, option D is incorrect because it squares the result rather than taking its square root. The correct expression in radical form that corresponds to 16 to the power of 3/2 is therefore option C, which can be written as (16^3)^(1/2).