SOLUTION: Simplify: {{{(8x^6y^6/4x^3y^12)^2}}}. I have tried subtracting the exponents, but I'm not sure how to get rid of a negative exponent on the denomenator. Please help!! Thanks.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Simplify: {{{(8x^6y^6/4x^3y^12)^2}}}. I have tried subtracting the exponents, but I'm not sure how to get rid of a negative exponent on the denomenator. Please help!! Thanks.      Log On


   

Question 1010179: Simplify: %288x%5E6y%5E6%2F4x%5E3y%5E12%29%5E2. I have tried subtracting the exponents, but I'm not sure how to get rid of a negative exponent on the denomenator. Please help!! Thanks.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if the variable with the negative exponent is in the numerator, then place it in the denominator and make the exponent positive.

if the variable with the negative exponent is in the denominator, then place it in the numnerator and make the exponent positive.

your equation is %28%288+%2A+x%5E6+%2A+y%5E6%29+%2F+%284+%2A+x%5E3+%2A+y%5E12%29%29%5E2

this is equivalent to %28%288%2F4%29+%2A+%28x%5E6%29%2F%28x%5E3%29+%2A+%28y%5E6%29%2F%28y%5E12%29%29%5E2

simplify using the law of exponents that says that %28x%5Ea%29%2F%28x%5Eb%29+=+x%5E%28a-b%29 to get:

%282+%2A+x%5E3+%2A+y%5E-6%29%5E2

use the law of exponents that says that x%5E%28-a%29+=+1%2Fx%5Ea to get:

%282+%2A+x%5E3+%2A+1%2Fy%5E6%29%5E2

this is the same as %282%2Ax%5E3%2Fy%5E6%29%5E2

simplify to get:

%282%2Ax%5E3%2Fy%5E6%29%5E2 = %282%5E2%2A%28x%5E3%29%5E2%29%2F%28y%5E6%29%5E2 = 4%2Ax%5E6%2Fy%5E12

the other law of exponents that is used is:

%28x%5Ea%2Ax%5Eb%29%5Ec+=+x%5E%28ac%29%2Ax%5E%28bc%29