Why the properties of square roots are true only for negative exponents

I need it badly :(

You must have misunderstood your teacher, because your question doesn't make any sense.

Square roots are an example of FRACTIONAL exponents. Could this have something to do with your question?

** Update ****

You can say that the proposition is wrong.

Here is a property of square roots: √(x²) = |x| for all real x.

This property combines a square root with a positive power.

How about: For all positive x and y √(x)√(y) = √(xy). This is another property of square roots that has nothing to do with "negative exponents".

What properties?

A negative exponent usually means a fraction.

for example, x^(-4) is the same as 1 / x^4

If you are asked for the square root of x^(-4), you can do it EXACTLY the same way as you would for 1/x^4

Since a square root can be distributed over products and divisions, you could write:

√(x^(-4)) = √[ 1 / (x^4) ] = √1 / √x^4 = 1/x^2 = x^(-2)

The property (to take a square root of a power, you halve the exponent) works exactly the same when you do it directly with a negative exponent
√x^(-4) = x^(-4/2) = x^(-2)
or if you use the positive power
1 / √x^4 = 1 / x^(4/2) = 1 / x^2

Your assumption is wrong.

that's not true!!
what's the question ?