SOLUTION: what is the simplest form of (x^-2y^-3)over (x^2y^-1)^3

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Question 156859This question is from textbook College Algebra
: what is the simplest form of (x^-2y^-3)over (x^2y^-1)^3

This question is from textbook College Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E%28-2%29y%5E%28-3%29%29%2F%28x%5E2y%5E%28-1%29%29%5E3 Start with the given expression


%28%281%2F%28x%5E%282%29%29%29%281%2F%28y%5E%283%29%29%29%29%2F%28x%5E2%281%2Fy%29%29%5E3 Rewrite x%5E%28-2%29 as 1%2F%28x%5E%282%29%29. Rewrite y%5E%28-3%29 as 1%2F%28y%5E%283%29%29. Rewrite y%5E%28-1%29 as 1%2F%28y%5E%281%29%29=1%2Fy


%28%281%29%2F%28x%5E2%2Ay%5E3%29%29%2F%28%28x%5E2%29%2F%28y%29%29%5E3 Combine the fractions


%28%281%29%2F%28x%5E2%2Ay%5E3%29%29%2F%28%28x%5E6%29%2F%28y%5E3%29%29 Distribute the outer exponent 3 to the inner exponents in the denominator


%28%281%29%2F%28x%5E2%2Ay%5E3%29%29%2A%28%28y%5E3%29%2F%28x%5E6%29%29 Multiply the first fraction by the reciprocal of the second fraction.


%28%281%29%2F%28x%5E%282%2B6%29%2Ay%5E3%29%29 Combine and multiply . Note: %28x%5E2%29%28x%5E6%29=x%5E%282%2B6%29


%28y%5E3%29%2F%28x%5E%288%29y%5E3%29 Add


%28y%5E%283-3%29%29%2F%28x%5E%288%29%29 Divide by subtracting the exponents.


%28y%5E%280%29%29%2F%28x%5E%288%29%29 Subtract


%281%29%2F%28x%5E%288%29%29 Simplify


So %28x%5E%28-2%29y%5E%28-3%29%29%2F%28x%5E2y%5E%28-1%29%29%5E3 simplifies to %281%29%2F%28x%5E%288%29%29


In other words, %28x%5E%28-2%29y%5E%28-3%29%29%2F%28x%5E2y%5E%28-1%29%29%5E3=%281%29%2F%28x%5E%288%29%29 where x%3C%3E0 or y%3C%3E0