Question

Simplify `((x^-1y^4)/(x^2y^7))^-3` ?

Answer 1

`((x^-1y^4)/(x^2y^7))^-3=x^9y^9`

Explanation:

The expression as written in the (original - before restoration) question is ambiguous as it is unclear whether denominator should be read as the product of the `x^2` and `y^7` terms or only the `x^2`.

I have chosen to interpret the expression as `((x^-1y^4)/(x^2y^7))^-3`

Two rules of indices will apply here:

(i) `a^m xx a^n = a^(m+n)`
(ii) `(a^m)^n = a^(m xx n)`

`((x^-1y^4)/(x^2y^7))^-3 = (x^(-1-2) xx y^(4-7))^-3` [Rule (i)]

`=(x^-3 xx y^-3)^-3`

`=x^9y^9` [Rule (ii)]