SOLUTION: Simplify the expression (3x^(-4)y^(5))/((2x^(3)y^(-7))^(-2)) and write the answer using only positive exponents. Please help!!! Thanks!

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Simplify the expression (3x^(-4)y^(5))/((2x^(3)y^(-7))^(-2)) and write the answer using only positive exponents. Please help!!! Thanks!      Log On


   

Question 549592: Simplify the expression (3x^(-4)y^(5))/((2x^(3)y^(-7))^(-2)) and write the answer using only positive exponents.
Please help!!! Thanks!
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%5E%28-4%29y%5E%285%29%29%2F%28%282x%5E%283%29y%5E%28-7%29%29%5E%28-2%29%29
We will first use our exponent law that says %28a%5Em%29%5En=a%5E%28m%2An%29
To get:
%283x%5E%28-4%29y%5E%285%29%29%2F%282%5E%28-2%29x%5E%283%2A-2%29y%5E%28-7%2A-2%29%29
%283x%5E%28-4%29y%5E%285%29%29%2F%282%5E%28-2%29x%5E%28-6%29y%5E%2814%29%29
Now we will use our negative exponent rule that says a%5E%28-x%29=1%2F%28a%5Ex%29 (basically if there is a negative exponent on the bottom bring it to the top and make the exponent positive and if it is on the top bring it to the bottom and make exponent positive:
%282%5E%282%293x%5E%286%29y%5E%285%29%29%2F%28y%5E%2814%29x%5E%284%29%29
%284%2A3x%5E%286%29y%5E%285%29%29%2F%28y%5E%2814%29x%5E%284%29%29
%2812%2Ax%5E%286%29y%5E%285%29%29%2F%28y%5E%2814%29x%5E%284%29%29
Now use the rule that says %28a%5Em%29%2F%28a%5En%29=a%5E%28m-n%29
%2812%2Ax%5E%286-4%29y%5E%285-14%29%29
%2812%2Ax%5E%282%29y%5E%28-9%29%29
And use the negative rule we used above to obtain:
%2812%2Ax%5E%282%29%29%2F%28y%5E%289%29%29