Question

Which is expression is equivalent to (x^-4y/x^-9y^5)^-2

Answer 1

`(y^8)/(x^(10))`

Explanation:

Given

`((x^(-4)y)/(x^(-9)y^5))^(-2)`

Required

The equivalent

Apply law of indices to the inner bracket

`(x^(-4--9)y^(1 -5))^(-2)`

`(x^(5)y^(-4))^(-2)`

Rewrite as:

`(1)/((x^(5)y^(-4))^2)`

Expand

`(1)/((x^(5*2)y^(-4*2)))`

`(1)/((x^(10)y^(-8)))`

Apply law of indices

`(y^8)/(x^(10))`