The problem is simple: simplify the square root of a square. Example:

(x

^{2})

^{(1/2) }

Here are steps that prove the answer is x:

(x

^{2})

^{(1/2)}= x

^{(1/2)}* x

^{(1/2)}= x

^{(1/2 + 1/2)}= x

^{(2/2)}= x

^{1}= x

However, consider the case where x = -4. By the above process:

((-4)

^{2})

^{(1/2)}= (-4)

^{(1/2)}* (-4)

^{(1/2)}= (-4)

^{(1/2 + 1/2)}= (-4)

^{(2/2)}= (-4)

^{1}= -4

However, I could also solve it this way:

((-4)

^{2})

^{(1/2)}= 16

^{(1/2)}= 4

One way, I get an answer of -4, the other way, I get an answer of 4, and every step is correct for both solutions.

Can someone please resolve this for me? Where did I do something that is incorrect?