-1=(-1)=(-1)^1=(-1)^2/2=((-1)^2)^1/2=(1)1/2=1
-1=1 
where am i make Mistake ?
wright it in a paper to understand better.

HI!!


The mistake camoes from the direct use of the PRINCIPAL SQUARE ROOT,
not that by definition for x >= 0, the square root is the number y
that satisfies y^2=x
For example 4^1/2 = 2 AND -2 because (-2)^2 = 4 and 2^2 = 4, depending
on the context of the problem you must select one of the results or
use both of them (for example when factoring a polinomial).

See for reference:
"Square root - Wikipedia, the free encyclopedia":
http://en.wikipedia.org/wiki/Square_root#Common_errors_involving_equations_with_the_principal_square_root_function


Hope this helps you. Feel free to request for a clarification if you need it.

Regards,
livioflores-ga

:)

Are you sure regarding ((-1)^2)^1/2?

Actually, the square root of a positive real number is going to be
associated with the absolute value.

For instance,

If X^2 = 9, for instance, then

X = |3| which means X= +3 AND X= -3

The same actually applies for all numbers but it is easiest to explain
and understand under the pretenses of whole real numbers.