SOLUTION: Rewrite with positive exponents. Assume that even roots are of nonnegative quantities and that all denominators are nonzero. (2x^2y^-1)^-6

Give the 2 an exponent of 1 so that everything
inside the parentheses has an exponent showing:



Remove the parentheses by multiplying every
exponent inside the parentheses, the 1, the 2, and the -1 
by the exponent -6 just outside the parentheses. When
you do that you have:



Put that over 1:



Now to get rid of a negative exponent in the
top (bottom) of a fraction, move the base and exponent
to the bottom (top) and change the sign of the
exponent to positive:

Bring the  to the bottom as 
Bring the  to the bottom as 
But leave the  in the top because it already
has a positive exponent.



One more thing 

So the final answer is:



Edwin