Answer
(a) Newton, $\mathrm{N}$ in base quantities is $\mathrm{[M^1L^1T^{-2}]}$.
(b) Equation $F=mv^2/r$ gives the same units for $\mathrm{N}$ as $F=ma$.
Work Step by Step
(a) We have, mass - $\mathrm{[M^1L^0T^0]}$.
for acceleration - $\mathrm{[M^0L^1T^{-2}]}$.
Their product, F has units $\mathrm{kg.m/s^2}$ and is $\mathrm{[M^1L^1T^{-2}]}$ in base quantities.
(b) Equation - $F=mv^2/r$
RHS - $mv^2/r$ will have units $\mathrm{kg.(m/s)^2/m}$ = $\mathrm{kg.m/s^2}$ which is the same as obtained in (a).
