Square roots and powers

Question

This is a rather silly question. In what order does one evaluate a combination of powers and fractional powers?

I have the question phrased:

$\sqrt{ 1/4^2 }$ OR ${ 1/4 }$? Which is greater?

I answered that it cannot be determined, because the ${ 1/4^2 }$ could be evaluated first and then the square root, yielding $\pm 1/4$. I understand it could also be the multiplication of exponents, yielding +1/4.

Which of these is correct?

Answer 1

$\sqrt x$ means, by definition, the positive number $r$ with $r^2=x$.

EDIT: make that, the non-negative number $r$ with $r^2=x$. Wouldn't want to leave out zero.

Answer 2

Here $(\sqrt \frac {1}{4^2})$ gives us only $\frac {1}{4}$ as root function has an absolute value associated with it .

Remember : $\sqrt {x^2}$ means, by definition, the *absolute value of x * number

answer : both aree same