import re, math,string
#Input   ->  new scale  ->  Output

unit1= "A^{-1} "#           x                    A^{-1}
unit2= "A"  #                   x                     A
unit3="A"  #                  x^2                  A^{2}
unit4= "A "  #                  1/x                  A^{-1}
unit5= "A^{0.5} " #        x^2                      A
unit9= "m^{1/2}" #         x^2               m

#If you don't recognize the pattern, give up and just put some parentheses around the unit and write the transoformation:

unit6= "m/s"  #                x^2               (m/s)^{2}
unit7= "m/s^{2}" #         1/x                 (m/s^{2})^{-1}
unit8= "m/s^{4}" #         x^2               (m/s^{4})^{2}


def UnitConvertion(pow,unit):
    if pow!=0:
        if string.find(unit, "^") !=-1:# if the unit contains a power ^
            unitSplitted= re.split("\^",unit)
            if string.find(unitSplitted[0],"/")!=-1 or\
             string.find(unitSplitted[0],"-")!=-1 : # find slash /
                if pow==1:
                    unit = unit
                else:
                    unit= "("+unit+")"+"^{"+str(pow)+"}"
            else:
                if string.find(unitSplitted[1],"{")!=-1:# if found a {
                    findPower= re.split("{",unitSplitted[1])
                    if string.find(findPower[1],"}")!=-1:# found }
                        unitPower= re.split("}",findPower[1])
                        if (string.find(unitPower[0],".")!=-1):
                            power= float(unitPower[0])*pow 
                        elif (string.find(unitPower[0],"/") !=-1 ): #power is a float
                            poweSplitted= re.split("/",unitPower[0])
                            power=pow*int(poweSplitted[0])/int(poweSplitted[1])
                        else:
                            power= int(unitPower[0])*pow   
                       
                        if power==1.0:
                           unit = unitSplitted[0]
                        elif power==0.5:
                            unit = unitSplitted[0]+"^{1/2}"  
                        elif power==-0.5:
                            unit = unitSplitted[0]+"^{-1/2}"  
                        else:
                            unit= unitSplitted[0]+"^{"+str(power)+"}"  
                else:
                     raise ValueError, "missing } in unit expression" 
                 
               
                 
        else:#no power
            if  pow !=1:
                unit="("+unit+")"+"^{"+str(pow)+"}"
    else:
        raise ValueError, "empty unit ,enter a power different from zero"
    return unit
if __name__ == "__main__": 
    print "this unit1 %s ,its power %s , and value %s"%(unit1,1,UnitConvertion(1,unit1))
    print "this unit2 %s ,its power %s , and value %s"%(unit2,1,UnitConvertion(1,unit2))
    print "this unit3 %s ,its power %s , and value %s"%(unit3,2,UnitConvertion(2,unit3))
    print "this unit4 %s ,its power %s , and value %s"%(unit4,-1,UnitConvertion(-1,unit4))
    print "this unit5 %s ,its power %s , and value %s"%(unit5,2,UnitConvertion(2,unit5))
    print "this unit6 %s ,its power %s , and value %s"%(unit6,2,UnitConvertion(2,unit6))
    print "this unit7 %s ,its power %s , and value %s"%(unit7,-1,UnitConvertion(-1,unit7))
    print "this unit8 %s ,its power %s , and value %s"%(unit8,2,UnitConvertion(2,unit8))
    print "this unit9 %s ,its power %s , and value %s"%(unit9,2,UnitConvertion(2,unit9))