Question 153366
<pre><font size = 4 color = "indigo"><b>
{{{((8x^2y^(-2))/(x^(-2)y)) ((4xy^2)^(-1)/x^2y)}}}

{{{((8x^2y^(-2))/(x^(-2)y)) ((4^1x^1y^2)^(-1)/x^2y)}}}

{{{((8x^2y^(-2))/(x^(-2)y)) ((4^(1*-1)x^(1*-1)y^(2*-1))/x^2y)}}}

{{{((8x^2y^(-2))/(x^(-2)y)) ((4^(-1)x^(-1)y^(-2))/x^2y)}}}

Bring all the negative exponentials across the fraction bar
and change their exponents signs to +

{{{((8x^2x^2)/(yy^2)) (1/4^1x^1x^2yy^2)}}}

Multiply numerators and denominators so there will be
just one fraction:

{{{(8x^2x^2)/(yy^2*4^1x^1x^2yy^2)}}}

{{{(8x^2x^2)/(y^1y^2*4^1x^1x^2y^1y^2)}}}

Add exponents of like variables:


{{{(8x^4)/(y^6*4^1x^3)}}}


Subtract exponents on the x's:

{{{(8x^1)/(y^6*4^1)}}}

Drop 1 exponents:


{{{(8x)/(y^6*4)}}}

The 4 cancels into the 8 and gives 2

{{{(2x)/(y^6)}}}

Edwin</pre>