SOLUTION: 1. Simplify the following expression, and rewrite it in an equivalent form with positive exponents. -18x^2 y^4 / 6x^7 y^2

Algebra ->  Exponents -> SOLUTION: 1. Simplify the following expression, and rewrite it in an equivalent form with positive exponents. -18x^2 y^4 / 6x^7 y^2       Log On


   

Question 373665: 1. Simplify the following expression, and rewrite it in an equivalent form with positive exponents.
-18x^2 y^4 / 6x^7 y^2
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28-18x%5E2%2Ay%5E4%29%2F%286x%5E7%2Ay%5E2%29
It can help to see how to simplify a fraction like this if you "unmultiply":
%28%28-18%29%2F6%29%2A%28x%5E2%2Fx%5E7%29%2A%28y%5E4%2Fy%5E2%29
Look at the above. If you were to multiply the three fractions, wouldn't you get the original fraction? And by writing the expression this way it should be clear what to do. -18/6 = -3. For the other two fractions we use the rule for exponents for division: Subtract the exponents. This gives us:
%28-3%29%2A%28x%5E%282-7%29%29%2A%28y%5E%284-2%29%29
which simplifies to:
%28-3%29%2A%28x%5E%28-5%29%29%2A%28y%5E2%29
Since we do not want negative exponents and since a%5E%28-q%29+=+1%2Fa%5Eq we can replace x%5E%28-5%29 with 1%2Fx%5E5:
%28-3%29%2A%281%2Fx%5E5%29%2A%28y%5E2%29
Now we can multiply:
%28%28-3%29%2F1%29%2A%281%2Fx%5E5%29%2A%28y%5E2%2F1%29
%28-3y%5E2%29%2Fx%5E5