SOLUTION: Negative integral Exponents; Perform the indicated operation; {{{(x^(-2)y^(-3))^(-1)/(x^(-2)+y^(-3))}}}

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Negative integral Exponents; Perform the indicated operation; {{{(x^(-2)y^(-3))^(-1)/(x^(-2)+y^(-3))}}}      Log On


   

Question 892712: Negative integral Exponents;
Perform the indicated operation;
%28x%5E%28-2%29y%5E%28-3%29%29%5E%28-1%29%2F%28x%5E%28-2%29%2By%5E%28-3%29%29
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E%28-2%29y%5E%28-3%29%29%5E%28-1%29%2F%28x%5E%28-2%29%2By%5E%28-3%29%29


On the top, multiply the two inner exponents times the one outer exponent to
remove the parentheses on top:

%28x%5E2y%5E3%29%2F%28x%5E%28-2%29%2By%5E%28-3%29%29

Rewrite each of the exponentials with negative exponents
as 1 over the exponential with the positive exponent:

%28x%5E2y%5E3%29%2F%281%2Fx%5E2%2B1%2Fy%5E3%29

Multiply top and bottom by red%28x%5E2y%5E3%29

red%28x%5E2y%5E3%29%28x%5E2y%5E3%29%2F%28red%28x%5E2y%5E3%29%281%2Fx%5E2%2B1%2Fy%5E3%29%29

Add exponents on top, distribute on bottom:

%28x%5E4y%5E6%29%2F%28y%5E3%2Bx%5E2%29 

Edwin