Question

How do you divide `(81r^10s^6)/((3r^2s)^4)`?

Answer 1

`=color(blue)(r^2s^2`

Explanation:

`(81r^10s^6)/(3r^2s)^color(blue)(4`

`=(81r^10s^6)/(3^color(blue)(4 ) r^(2*color(blue)(4)) s^color(blue)(4`

`=(cancel81r^10s^6)/(cancel81 r ^8s^4`

`=(r^10s^6)/(r^8s^4)`

• `color(blue)(a^m/a^n = a^(m-n)`

Applying this property to the exponents of `r and s`:

`=r^((10-8)) . s^((6-4))`

`=color(blue)(r^2s^2`