SOLUTION: Please help me solve the following question: Simplify the expression {{{((8x^2y^(-2))/(x^(-2)y)) ((4xy^2)^(-1)/x^2y)}}}

Algebra ->  Expressions-with-variables -> SOLUTION: Please help me solve the following question: Simplify the expression {{{((8x^2y^(-2))/(x^(-2)y)) ((4xy^2)^(-1)/x^2y)}}}      Log On


   

Question 153366: Please help me solve the following question:
Simplify the expression
%28%288x%5E2y%5E%28-2%29%29%2F%28x%5E%28-2%29y%29%29+%28%284xy%5E2%29%5E%28-1%29%2Fx%5E2y%29
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

%28%288x%5E2y%5E%28-2%29%29%2F%28x%5E%28-2%29y%29%29+%28%284xy%5E2%29%5E%28-1%29%2Fx%5E2y%29







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

%28%288x%5E2x%5E2%29%2F%28yy%5E2%29%29+%281%2F4%5E1x%5E1x%5E2yy%5E2%29

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

%288x%5E2x%5E2%29%2F%28yy%5E2%2A4%5E1x%5E1x%5E2yy%5E2%29

%288x%5E2x%5E2%29%2F%28y%5E1y%5E2%2A4%5E1x%5E1x%5E2y%5E1y%5E2%29

Add exponents of like variables:


%288x%5E4%29%2F%28y%5E6%2A4%5E1x%5E3%29


Subtract exponents on the x's:

%288x%5E1%29%2F%28y%5E6%2A4%5E1%29

Drop 1 exponents:


%288x%29%2F%28y%5E6%2A4%29

The 4 cancels into the 8 and gives 2

%282x%29%2F%28y%5E6%29

Edwin