ok for some reasons i can't get the answer for this dimensionally consistent.

1.The density of a substance is given by the equation:

ρ=70.5exp(8.27x10^-7P)

where:
ρ=Density [lbm/ft3]
P=Pressure[lbf/in2]

i) what are the units of 70.5 and 8.27x10^-7 ?
ii) calculate the density in g/cm3 for a pressure of 9.0x10^6 N/m2.
iii) derive a formula for ρ(g/cm3) as a function of P (N/m2).

Question

ok for some reasons i can't get the answer for this dimensionally consistent. 

1.The density of a substance is given by the equation: 

ρ=70.5exp(8.27x10^-7P) 

where: 
ρ=Density [lbm/ft3] 
P=Pressure[lbf/in2] 

i) what are the units of 70.5 and 8.27x10^-7 ? 
ii) calculate the density in g/cm3 for a pressure of 9.0x10^6 N/m2. 
iii) derive a formula for ρ(g/cm3) as a function of P (N/m2).

aaronq · Answer

i) The units of "8.27x10^-7P" should cancel, anti-logarithms should be unitless.

The units of "70.5" should be those of "$\rho$".

ii) plug in and solve

iii) it's already given in the question