Question

Simplify the following leaving your answer in positive index

1) (x/y)^-4 x (y/x)^8

Answer 1

`((x)/(y))^(-4) * ((y)/(x))^8 = ((y)/(x))^{12`

Explanation:

Given

`((x)/(y))^(-4) * ((y)/(x))^8`

Required

Determine the solution to this

`((x)/(y))^(-4) * ((y)/(x))^8`

In law of incides:

`(a)/(b) = (b)/(a)^(-1)`

This implies that:

`((x)/(y))^(-4) * ((y)/(x))^8` is equivalent to:

`((y)/(x))^(-(-4)) * ((y)/(x))^8`

`((y)/(x))^(4) * ((y)/(x))^8`

Apply first law of indices:

`((y)/(x))^{4+8`

`((y)/(x))^{12`

Hence:

`((x)/(y))^(-4) * ((y)/(x))^8 = ((y)/(x))^{12`