For a term of form: [MASS^x][LENGTH^y][TIME^z]{([Meter]/[Farad])^s}:
          ENTRY        has dimensions:            x    y    z    s
AUN = Atomic unit of ;  * = factor of rotation?   .    .    .    .
[2Pi]=2 times [Pi]                                0    0    0    0*
[2af]=[2Pi][f0] = AUN frequency            scnd   0    0   -1    0*
[4Pi]=4 times [Pi]                                0    0    0    0*
[18P]=AUN Electric Polarizability  C2uljuulM2tr   0    3    0   -1
[19H]=AUN 1st Hyperpolarizability  C3ulj2ulM3tr -1/2  3/2   1  -3/2
[20H]=AUN 2nd Hyperpolarizability  C4ulj3ulM4tr  -1    4    2   -2
[23M]=AUN magnetizability              Juult2la   0    5   -2   -1
[29H]=[H0][[4Pi]{[aa]^2}               Amprmetr  1/2  1/2  -2  -1/2*
[43P]=(4 times [Pi])/3                            0    0    0    0*
[a ]= Acceleration                     Metrs2nd   0    1   -2    0
[a0]= AUN length = Bohr atom radius        Metr   0    1    0    0
[A ]= Area                                 M2tr   0    2    0    0
[A0]= AUN area = [4Pi]([a0]^2)             M2tr   0    2    0    0*
[aa]= Fine structure constant                     0    0    0    0
[aBH]=[FBH]/[PM]                       Metrs2nd   0    1   -2    0
[aD]= Absorbed dose               Gryy=Juulkgrm   0    2   -2    0
[ae]= [Fe]/[Me]                        Metrs2nd   0    1   -2    0
[amu]=Atomic mass unit  = [10^-26.7797510 Kgrm]   1    0    0    0
[An]= Avagadro constant        molecules/[Mool]   0    0    0    0
[aR]= Absorbed dose rate               Gryyscnd   0    2   -3    0
[b ]= Mass frequency                   Kgrmscnd   1    0   -1    0
[B ]= Magnetic flux density       Tsla=m2trWebr  1/2 -3/2   0   1/2*
[B0]= AUN Magnetic flux density            Tsla  1/2 -3/2   0   1/2*
[BHR]=[G]/[c^2]                        kgrmMetr  -1    1    0    0
[Bk]= Boltzmann constant               degkJuul   1    2   -2    0
[Bm]= Bohr Magneton                    AmprM2tr  1/2  7/2  -2  -1/2*
[c ]= Speed of light in vacuum         Metrscnd   0    1   -1    0
[c^2]= [c] times [c]                   M2trs2nd   0    2   -2    0
[C ]= Capacitance                 Frad=Cuulvltt   0    1    0   -1
[Cm]= Compressibility = ([V]/[Pr])/[V]     pscl  -1    1    2    0
[Cn]= Conductance                     Smns=ohmm   0    1   -1   -1
[cQ]= Circulation quantum              M2trscnd   0    2   -1    0*
[Ct]= Conductivity                     metrSmns   0    0   -1   -1
[Cw]= Compton wavelength                   Metr   0    1    0    0
[d ]= Magnetic constant, permeability  Hnrymetr   0   -2    2    1*
[D ]= Mass density                     Kgrmm3tr   1   -3    0    0
[De]= Dose equivalent             Svrt=Juulkgrm   0    2   -2    0
[Dp]= [Mp]/([4/3][Pi]{[Rp]^3})         Kgrmm3tr   1   -3    0    0
[DQ]= [Me]/([4/3][Pi]{[Re]^3})         Kgrmm3tr   1   -3    0    0
[e ]= Energy, work, heat          Juul=MetrNwtn   1    2   -2    0
[E ]= Electric field strength          metrVltt  1/2 -1/2  -1   1/2
[E0]= AUN electric field strength      metrVltt  1/2 -1/2  -1   1/2
[eD]= Energy density                   Juulm3tr   1   -1   -2    0
[Ed]= Electric flux density            Cuulm2tr  1/2 -1/2  -1  -1/2
[Ef]= Electric flux                        Cuul  1/2  3/2  -1  -1/2
[Eg]= Electric field gradient          m2trVltt  1/2 -3/2  -1   1/2
[Eg0]=AUN electric field gradient      m2trVltt  1/2 -3/2  -1   1/2
[Ep]= Electric polarization            metrVltt  1/2 -1/2  -1   1/2
[eS]= Specific energy                  Juulkgrm   0    2   -2    0
[eV]= Electron-volt     = [10^-18.7952897 Juul]   1    2   -2    0
[Ex]= Radiation exposure               Cuulkgrm -1/2  3/2  -1  -1/2
[f ]= Frequency                       Hrtz=scnd   0    0   -1    0
[f0]= Bohr electron orbital frequency      Hrtz   0    0   -1    0
[F ]= Force                                Nwtn   1    1   -2    0
[FBH]=[G]{[PM]^2}/{[PL]^2} = [c^4]/[G]     Nwtn   1    1   -2    0
[Fe]= [Ke]([Q0]^2)/([a0]^2)                Nwtn   1    1   -2    0
[Fg]= [G][Me][Mp]/([a0]^2)                 Nwtn   1    1   -2    0
[Fge]=[G]([Me]^2)/([a0]^2)                 Nwtn   1    1   -2    0
[Fgp]=[G]([Mp]^2)/([a0]^2)                 Nwtn   1    1   -2    0
[FPC]=[d]{[PC]^2}                          Nwtn   1    1   -2    0
[FPQ]=[Ke]{[PQ]^2}/{[PL]^2}                Nwtn   1    1   -2    0
[FPX]=[Ke]{[PX]^2}/{[PL]^2}                Nwtn   1    1   -2    0
[g ]= Earth acceleration of gravity    kgrmNwtn   0    1   -2    0
[G ]= Gravitational constant       k2rmM2trNwtn  -1    3   -2    0
[G0]= Conductance quantum             Smns=ohmm   0    1   -1   -1
[Gev]= [10^9 eV]         = [10^-9.7952897 Juul]   1    2   -2    0
[Gy]= Gyromagnetic ratio           AmprkgrmScnd -1/2  3/2  -1  -1/2*
[Gye]=Gyromagnetic ratio of electron   Cuulkgrm -1/2  3/2  -1  -1/2*
[Gyn]=Gyromagnetic ratio of neutron    Cuulkgrm -1/2  3/2  -1  -1/2*
[Gyp]=Gyromagnetic ratio of proton     scndtsla -1/2  3/2  -1  -1/2*
[h ]= Planck constant                  JuulScnd   1    2   -1    0
[H ]= Magnetic field strength          Amprmetr  1/2  1/2  -2  -1/2*
[H0]= AUN magnetic field strength      Amprmetr  1/2  1/2  -2  -1/2*
[hB]= AUN action = [h]/[2Pi]           JuulScnd   1    2   -1    0
[He]= AUN energy                           Juul   1    2   -2    0
[Hu]= Hubble constant                      Hrtz   0    0   -1    0
[i ]= Current                     Ampr=Cuulscnd  1/2  3/2  -2  -1/2
[i0]= AUN current                          Ampr  1/2  3/2  -2  -1/2
[I ]= Inductance                  Hnry=amprWebr   0   -1    2    1*
[Im]= Impulse                      KgrmMetrscnd   1    1   -1    0
[Ir]= Irradiance                       m2trWaat   1    0   -3    0
[j ]= Current density                  Amprm2tr  1/2 -1/2  -2  -1/2
[Jf]= Josephson constant          Hrtzvltt=webr -1/2 -1/2   0  -1/2*
[k ]= Electric constant, permittivity  Fradmetr   0    0    0   -1*
[Ke]= 1/(4[Pi][k])                     fradMetr   0    0    0    1*
[Kev]= [10^3 eV]        = [10^-15.7952897 Juul]   1    2   -2    0
[Kv]= Kinematic viscosity              M2trscnd   0    2   -1    0
[L ]= Length                               Metr   0    1    0    0
[Lcn]=Loschmidt constant                   m3tr   0   -3    0    0
[m ]= Magnetization                    Amprmetr  1/2  1/2  -2  -1/2*
[M ]= Mass                                 Kgrm   1    0    0    0
[Ma]= Mass of alpha particle               Kgrm   1    0    0    0
[Md]= Mass of deuteron                     Kgrm   1    0    0    0
[Me]= AUN mass = Mass of electron          Kgrm   1    0    0    0
[Mev]= [10^6 eV]        = [10^-12.7952897 Juul]   1    2   -2    0
[Mh]= Mass of helion                       Kgrm   1    0    0    0
[mI]= Moment of inertia                KgrmM2tr   1    2    0    0
[Mm]= Mass of muon                         Kgrm   1    0    0    0
[mma]=Electron magnetic moment anomaly            0    0    0    0
[Mn]= Mass of neutron                      Kgrm   1    0    0    0
[Mp]= Mass of proton                       Kgrm   1    0    0    0
[Mt]= Mass of tau particle                 Kgrm   1    0    0    0
[Mtt]=Mass of triton                       Kgrm   1    0    0    0
[N ]= Wave number                          metr   0   -1    0    0
[Nm]= Nuclear magneton                 Juultsla  1/2  7/2  -2  -1/2*
[O ]= Origin                                      0    0    0    0
[p ]= Momentum                     KgrmMetrscnd   1    1   -1    0
[p0]= AUN Momentum                 KgrmMetrscnd   1    1   -1    0
[PA]= [4Pi]([PL]^2)                        M2tr   0    2    0    0*
[PB]= {[PM]/([k]{[PL]^3})}^.5              Tsla  1/2 -3/2   0   1/2*
[PC]= Planck current                       Ampr  1/2  3/2  -2  -1/2
[PE]= Planck energy                        Juul   1    2   -2    0
[Pf]= Planck frequency                     scnd   0    0   -1    0
[phi]=Natural proportion constant                 0    0    0    0
[Pi]= Circle circumference to diameter ratio      0    0    0    0*
[PK]= Planck temperature                   Degk   0    0    0    0
[PL]= Planck length                        Metr   0    1    0    0
[PM]= Planck mass                          Kgrm   1    0    0    0
[Pp]= Planck momentum              KgrmMetrscnd   1    1   -1    0
[PPw]=Planck power                         Waat   1    2   -3    0
[PQ]= Planck charge = ([hB][c][k])^.5      Cuul  1/2  3/2  -1  -1/2
[Pr]= Pressure, stress            Pscl=m2trNwtn   1   -1   -2    0
[PRL]=[2Pi][PL]                            Metr   0    1    0    0*
[PT]= Planck time                          Scnd   0    0    1    0
[Pu0]=[PC]{[PL]^2} =Planck mag moment  AmprM2tr  1/2  7/2  -2  -1/2*
[PV]= ([4Pi]/3)([PL]^3)                    M3tr   0    3    0    0*
[Pw]= Power                       Waat=Juulscnd   1    2   -3    0
[Pw0]=AUN power                   Waat=Juulscnd   1    2   -3    0
[PX]= ([hB][c][4Pi][k])^.5                 Cuul  1/2  3/2  -1  -1/2
[q ]= Electric dipole moment           CuulMetr  1/2  5/2  -1  -1/2
[q0]= AUN electric dipole moment       CuulMetr  1/2  5/2  -1  -1/2
[Q ]= Charge                      Cuul=AmprScnd  1/2  3/2  -1  -1/2
[Q0]= AUN charge = Electron charge         Cuul  1/2  3/2  -1  -1/2
[qD]= Electric quadrapole moment       CuulM2tr  1/2  7/2  -1  -1/2
[qD0]=AUN electric quadrapole moment   CuulM2tr  1/2  7/2  -1  -1/2
[QD]= Charge density                   Cuulm3tr  1/2 -3/2  -1  -1/2
[QD0]=AUN charge density               Cuulm3tr  1/2 -3/2  -1  -1/2
[Q/M]=Specfic Charge                   Cuulkgrm -1/2  3/2  -1  -1/2
[QeM]=[Q0]/[Me]                        Cuulkgrm -1/2  3/2  -1  -1/2
[r ]= Resistivity                      MetrOhmm   0    0    1    1
[R ]= Resistance                  Ohmm=amprVltt   0   -1    1    1
[Ra]= Radionuclide activity           Bqrl=scnd   0    0   -1    0
[Rc]= Rydberg constant                     metr   0   -1    0    0
[Re]= Classical electron radius            Metr   0    1    0    0
[Rgc]=Molar gas constant           degkJuulmool   1    2   -2    0
[RK]= von Klitzing constant                Ohmm   0   -1    1    1
[Rn]= Neutron Compton wavelength           Metr   0    1    0    0
[Rp]= Proton Compton wavelength            Metr   0    1    0    0
[S ]= Poynting vector                  m2trWaat   1    0   -3    0
[St]= Surface tension                  Juulm2tr   1    0   -2    0
[T ]= Time                                 Scnd   0    0    1    0
[Tc]= Thompson cross section               M2tr   0    2    0    0*
[Tev]= [10^12 eV]       = [10^-18.7952897 Juul]   1    2   -2    0
[Tp]= Proton characteristic time           Scnd   0    0    1    0
[Tr]= Torque                           MetrNwtn   1    2   -2    0*
[u ]= Magnetic dipole moment           AmprM2tr  1/2  7/2  -2  -1/2*
[u0]= AUN magnetic dipole moment       AmprM2tr  1/2  7/2  -2  -1/2*
[ud]= Deuteron magnetic moment         AmprM2tr  1/2  7/2  -2  -1/2*
[ue]= Electron magnetic moment         AmprM2tr  1/2  7/2  -2  -1/2*
[um]= Muon magnetic moment             AmprM2tr  1/2  7/2  -2  -1/2*
[un]= Neutron magnetic moment          AmprM2tr  1/2  7/2  -2  -1/2*
[up]= Proton magnetic moment           AmprM2tr  1/2  7/2  -2  -1/2*
[v ]= Velocity                         Metrscnd   0    1   -1    0
[v0]= AUN velocity                     Metrscnd   0    1   -1    0
[V ]= Volume                               M3tr   0    3    0    0
[V0]= ([4Pi]/3)([a0]^3)                    M3tr   0    3    0    0*
[Vi]= Dynamic viscosity            m2trNwtnScnd   1   -1   -1    0
[Vmi]=Ideal gas molar volume           M3trmool   0    3    0    0*
[vT]= Voltage                     Vltt=Cuulfrad  1/2  1/2  -1   1/2
[vT0]=AUN voltage                 Vltt=amprWaat  1/2  1/2  -1   1/2
[V]/[M]=Specific volume                kgrmM3tr  -1    3    0    0*
[w ]= Magnetic flux               Webr=ScndVltt  1/2  1/2   0   1/2*
[w0]= Magnetic flux quantum                Webr  1/2  1/2   0   1/2*
[Y ]= Angular momentum             KgrmM2trscnd   1    2   -1    0*
[z ]= Impedance                            Ohmm   0   -1    1    1
[z0]= Intrinsic impedance of vacuum        Ohmm   0   -1    1    1
Ampere : Ampr     Joule: Juul     Newton : Nwtn     Steradian: Strr
Coulomb: Cuul     Katal: Katl     Ohm    : Ohmm     Sievert  : Svrt
Farad  : Frad     Lumen: Lmen     Pascal : Pscl     Tesla    : Tsla
Gray   : Gryy     Lux  : Luxx     Radian : Radn     Volt     : Vltt
Henry  : Hnry     Meter: Metr     Second : Scnd     Watt     : Waat
Hertz  : Hrtz     Mole : Mool     Siemens: Smns     Weber    : Webr
Becquerel: Bcql     Hrtz = scnd     Scnd = hrtz     Kilogram : Kgrm
degrees Centigrade: Degc    Candela = Cnda     degrees Kelvin: Degk
   here is the numerical value as a power of ten for :
[2]  + 0.3010300 [d ] - 5.9007901 [Lcn]+25.4292322 [PV]-103.7506794
[3]  + 0.4771213 [E0] +11.7111495 [Ma] -26.1775275 [Pw0]- 0.7441541
[4]  + 0.6020600 [Eg0]+21.9875484 [Md] -26.4757878 [PX] -17.7268723
[Pi] + 0.4971499 [f0] +15.8182050 [Me] -30.0405111 [q0] -29.0716885
[2Pi]+ 0.7981799 [FBH]+44.0817422 [Mh] -26.3004734 [Q0] -18.7952896
[4Pi]+ 1.0992099 [Fe] - 7.0841401 [Mm] -27.7250271 [qD0]-39.3480874
[18P]-40.7828380 [Fg] -46.4387750 [mma]- 2.9356722 [QD0]+12.0339070
[19P]-52.4939875 [Fge]-49.7026838 [Mn] -26.7760040 [QeM]+11.2452215
[20H]-64.2051370 [Fgp]-43.1748662 [Mp] -26.7766023 [Rc] + 7.0403543
[23M]-28.1028659 [FPC]+44.0817422 [Mt] -26.4992464 [Re] -14.5500682
[29H]+ 8.0974941 [FPQ]+42.9825322 [Mtt]-26.3003915 [Rgc]+ 0.9198342
[2af]+16.6163849 [FPX]+44.0817422 [Nm] -26.2966413 [RK] + 4.4118352
[a0] -10.2763989 [G ] -10.1744595 [p0] -23.7005250 [Rn] -14.8795607
[A0] -19.4535879 [G0] - 4.1108052 [PA] -68.4826355 [Rp] -14.8789625
[aa] - 2.1368347 [Gye]+11.2457248 [PB] +53.8813988 [Tc] -28.1770178
[aBH]+51.7445641 [Gyn]+ 8.2630373 [PC] +24.9912662 [Tp] -23.3557831
[ae] +22.9563709 [Gyp]+ 8.4273598 [PE] + 9.2908195 [u0] -22.7317025
[An] +23.7797510 [h ] -33.1787440 [Pf] +43.2677434 [ue] -23.0322291
[B0] + 5.3711635 [H0] +11.2719536 [phi]+ 0.2089876 [um] -25.3477103
[BHR]-27.1281008 [hB] -33.9769239 [PK] +32.1507363 [un] -26.0149166
[Bk] -22.8599168 [He] -17.3605390 [PL] -34.7909227 [up] -25.8505941
[Bm] -23.0327325 [Hu] -17.6028630 [PM] - 7.6628219 [v0] + 6.3399860
[c ] + 8.4768207 [i0] - 2.1789047 [Pp] + 0.8139988 [V0] -30.2071080
[c^2]+16.9536414 [Jf] +14.6844844 [PPw]+52.5585629 [vT0]+ 1.4347506
[cQ] - 3.4392630 [k ] -11.0528513 [PQ] -18.2764773 [w0] -14.6844844
[Cw] -11.6150537 [Ke] + 9.9536414 [Pu0]-44.5905793 [z0] + 2.5760306
[Me]/[Mp] = [Nm]/[Bm] = [Rp]/[Cw] = [aa][Rp]/{[Re][2Pi]} -3.2639088
[PX][PF] -25.5408711  [4Pi][aa] -1.0376248 [4Pi]{[aa]^2} -3.1744595