Answer
The length of the Neptunian year is 160 Earth years.
Work Step by Step
$(\frac{T_{N}}{T_{E}})^2 = (\frac{s_N}{s_E})^3$
$(\frac{T_{N}}{T_{E}}) = (\frac{s_N}{s_E})^{3/2}$
$(\frac{T_{N}}{T_{E}}) = (\frac{4.5 \times 10^9 ~km}{1.5\times 10^8 ~km} )^{3/2}$
$(\frac{T_{N}}{T_{E}}) = (30)^{3/2}$
$(\frac{T_{N}}{T_{E}}) = 164$
$T_N = 164\times T_E = 164\approx160 ~years$
The length of the Neptunian year is 160 Earth years.