Question

How do you simplify `[(6x^-4z^3)/(2xz^-3)]^-1`?

Answer 1

`x^5/(3z^6)`

Explanation:

There are a number of laws of indices involved here.
Do one step at a time.

`[(6x^-4z^3)/(2xz^-3)]^color(red)(-1) larr` Flip the fraction. Index changes sign.

`[(cancel2xcolor(blue)(z^-3))/(cancel6^3color(magenta)(x^-4)z^3)]^color(red)(+1)larr " cancel numbers, " x^-m = 1/x^m`

`(xcolor(magenta)(x^4))/(3z^3color(blue)(z^3)) " "larr` add indices of like bases.

`x^5/(3z^6)`