SOLUTION: how would i solve the problem (2x^3y^-2)^2 over (x^-2y^3)

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Question 253307: how would i solve the problem (2x^3y^-2)^2 over (x^-2y^3)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

%282x%5E3y%5E%28-2%29%29%5E2+%2F+%28x%5E%28-2%29y%5E3%29

give the 2 the understood exponent 1

%282%5E1%2Ax%5E3%2Ay%5E%28-2%29%29%5E2+%2F+%28x%5E%28-2%29%2Ay%5E3%29

Remove the parentheses on top by multiplying every inner
exponent by the outer exponent:


%282%5E%281%2A2%29x%5E%283%2A2%29y%5E%28-2%2A2%29%29%2F%28x%5E%28-2%29y%5E3%29

%282%5E2x%5E6y%5E%28-4%29%29%2F%28x%5E%28-2%29y%5E3%29

Rewrite 2%5E2 as 4

%284x%5E6y%5E%28-4%29%29%2F%28x%5E%28-2%29y%5E3%29

Move the y%5E%28-4%29 from the
top to the bottom by changing the sign of the
negative exponent to positive.

%284x%5E6%29%2F%28y%5E4%2Ax%5E%28-2%29%2Ay%5E3%29+

Now move the x%5E%28-2%29 from the bottom
to the top by changing the sign of the
negative exponent to positive


%284x%5E6%2Ax%5E2%29%2F%28y%5E4%2Ay%5E3%29

Add the exponents of the x's on top and add the
exponents of the y's on the bottom

%284x%5E8%29%2F%28y%5E7%29

Edwin