Question

In radical form, the expression 1/x^2 is equivalent to ______.

A) x^2
B) square root x
C) (1/2)^x
D) x square root 1/2

Answer 1

The expression 1/x^2 is not directly listed in any of the answer choices provided. It is correctly converted to x^-2 which is in radical form equivalent to the 1/x, but this option is not available among the choices A-D.

Step-by-step explanation:

In radical form, the expression 1/x^2 is equivalent to the radical expression x-2. To understand this, remember the negative exponent rule which states that xn is equal to 1/x-n. Therefore, 1/x2 is simply x-2. Since taking the square root of a number is the same as raising it to the 1/2 power, we see that the square root of x-2 is x-1 which is equivalent to 1/x. However, as the options provided do not include this form, the correct answer would be none of the given options A, B, C, or D.