An easy way to remember the dimensions of the newton is to recall that it is a unit of force.

Force is a mass times an acceleration.

F = M x a
a = d v d^{2}x
--- = ---
d t d t^{2}

so the dimension has to be

Mass (M)times

Length(L) divided by (

Time(t) squared)

ML
---
T^{2}

or in SI units this becomes kg m s^{-2}