$M ^1=\left( ML ^2 T ^{-1}\right)^{ x }\left( LT ^{-1}\right)\left( M ^{-1} L ^3 T ^{-2}\right)^Z$

$M ^1 L ^0 T ^0= M ^{ x - z } L ^{2 x + y +3 z} T ^{- x - y -2 z}$

on comparing both side

$x-z=1$

$2 x+y+3 z=0$

$-x-y-2 z=0$

On solving above equations we get

$x=\frac{1}{2} \quad y=\frac{1}{2} \quad z=\frac{-1}{2}$