Answer
[T]$^{-3}$
Work Step by Step
$v = \frac{1}{3}zxt^{2}$
$z = \frac{3v}{xt^{2}} $ = $3v \times \frac{1}{x} \times \frac{1}{t^{2}} $
Dimensions of z
= $ \frac{[L]}{[T]} \times \frac{1}{[L]} \times \frac{1}{[T]^{2}} $
= $\frac{1}{[T]^{3}}$
= [T]$^{-3}$
