Answer
Energy is represented in Joules (J), which is equal to $kg \space m^2/s^2$
$\frac{1}{2} mv^2 : (kg) (m/s)^2 = kg \space m^2 / s^2 $
$\frac 32 PV: (kg/(s^2m))(m^3) = kg \space m^2 / s^2$
Work Step by Step
The SI unit for each term is:
$m : kg$
$v : m/s$
$a : m/s^2$
$A = m^2$
$P = F /A = (m \times a)/ A :(kg) \times (m/s^2)/(m^2) = (kg \space m/s^2)/m^2 = kg/(s^2m)$
$V : m^3$
Energy is represented in Joules (J), which is equal to $kg \space m^2/s^2$
Thus: $\frac{1}{2} mv^2 : (kg) (m/s)^2 = kg \space m^2 / s^2 $
And: $\frac 32 PV: (kg/(s^2m))(m^3) = kg \space m^2 / s^2$
