2x^-2y^0(x^2y^0-4x^-6y^4

Is this what you mean?

2x-2y0(x2y0 - 4x-6y4)

If so, replace both y0's by 1.

2x-2·1(x2·1 - 4x-6y4)

2x-2(x2 - 4x-6y4)

Now use the distributive principle:

2x-2·x2 - 8x-2·4x-6y4

Add the exponents of x in the first term: -2 + 2 = 0,
so replace x-2·x2 by x0

2x0 - 8x-2·x-6y4

But x0 is just 1, so replace x0 by 1

2·1 - 8x-2x-6y4

2 - 8x-2x-6y4

Now add the exponents of x in the second term:
-2 + -6 = -8. so replace x-2x-6 by x-8

2 - 8x-8y4

To get rid of the negative exponent in x-8, replace
x-8 by 1/x8

2 - 8(1/x8)y4

Simplify the second term:

2 - 8y4/x8
 
Edwin
AnlytcPhil@aol.com