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

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Answer 1 · 2016-09-01T20:17:12

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

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.

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

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