Expert Answers
kingattaskus12 eNotes educator| Certified Educator

Move the minus sign from the denominator to the front of the expression.

`-(8x^(-3)-y^(-1))/(2x^6 y^(-4))`


Cancel the common factor of `2` in `-(8x^(-3)-y^(-1))/(2x^6 y^(-4))`  since

`-(8x^(-3)-y^(-1))/(2x^6 y^(-4)) = ((-4y^3 * 2))/((x^9 * 2))`


Remove the common factors that were cancelled out.

`-(4y^3)/(x^9)`


Cancel the common factor of `x^-3`  in `-(4y^3)/(x^9)`  since
`-(4y^3)/(x^9) = ((-4y^3 * x^-3))/((x^9 * x^-3))`

`-(4y^3)/x^(9^9)`


Remove the common factors that were cancelled out.

`-(4y^3)/x^9`


Cancel the common factor of `y^-4`  in `-(4y^3)/x^9`  since `-(4y^3)/x^9 = ((-4y^3 * y^-4))/((x^9 * y^-4))`

`-(4y^(3^3))/(x^9)`


Reduce the expression `-(8x^(-3) y^(-1))/(2x^6 y^(-4))`  by removing a factor of `2x^(-3) y^(-4)`  from the numerator and denominator.

`-(4y^3)/x^9`  

llltkl | Student

`(8x^(-3)y^(-1))/(-2x^6y^(-4))`

Divide both numerator and denominator by -2 and sum up the indices of like terms according to the law of indices,

`=-(4x^((-3-6))y^((-1+4)))` (since `p^m/p^n=p^((m-n))` )

`=-4x^(-9)y^3`

`=-4y^3/x^9`