Question

Which of the following expressions is equivalent to 16x^2)^1/2?

A. 4x
B. 8x
C. 2x
D. 16x

Answer 1

The expression equivalent to (16x^2)^1/2 is 4x, obtained by taking the square root of the coefficient (16) and the variable term (x^2) separately to result in 4x. Therefore, the correct answer is A. 4x.

Step-by-step explanation:

The student has asked which expression is equivalent to (16x^2)^1/2. We can simplify this expression by taking the square root of both the coefficient and the variable separately. The square root of 16 is 4, and the square root of x^2 is x. Thus, the equivalent expression is 4x.

Here is the step-by-step explanation:

1. Start with the given expression: (16x^2)^1/2.
2. Apply the square root to 16 and x^2 separately because of the property √(ab) = √a √b, where a and b are non-negative.
3. Calculate the square root of 16, which is 4.
4. Calculate the square root of x^2, which is x.
5. Combine both results to get 4x.

Therefore, the correct answer is A. 4x.