>>> math.pow(-3, float(1)/3)
nan

-math.pow(3, float(1)/3)

if x > 0:
    return math.pow(x, float(1)/3)
elif x < 0:
    return -math.pow(abs(x), float(1)/3)
else:
    return 0

import numpy
import math
def cuberoot( z ):
    z = complex(z)
    x = z.real
    y = z.imag
    mag = abs(z)
    arg = math.atan2(y,x)
    return [ mag**(1./3) * numpy.exp( 1j*(arg+2*n*math.pi)/3 ) for n in range(1,4) ]

def cuberoot( z ):
    z = complex(z)
    x = z.real
    y = z.imag
    mag = abs(z)
    arg = math.atan2(y,x)
    resMag = mag**(1./3)
    resArg = [ (arg+2*math.pi*n)/3. for n in range(1,4) ]
    return [  resMag*(math.cos(a) + math.sin(a)*1j) for a in resArg ]

math.pow(abs(x),float(1)/3) * (1,-1)[x<0]

import cmath

x, t = -3., 3  # x**(1/t)

a = cmath.exp((1./t)*cmath.log(x))
p = cmath.exp(1j*2*cmath.pi*(1./t))

r = [a*(p**i) for i in range(t)]

import math
def cubic_root(x):
    return math.copysign(math.pow(abs(x), 1.0/3.0), x)

from ctypes import *
libm = cdll.LoadLibrary('libm.so.6')
libm.cbrt.restype = c_double
libm.cbrt.argtypes = [c_double]
libm.cbrt(-8.0)

-2.0

>>> from scipy.special import cbrt
>>> cbrt(-3)
-1.4422495703074083

cbrt = lambda n: n/abs(n)*abs(n)**(1./3)

def cubic_root(nr):
   if nr<0:
     return -math.pow(-nr, float(1)/3)
   else:
     return math.pow(nr, float(1)/3)

import numpy as np

x = np.array([-81,25])
print x
#>>> [-81  25]

xRoot5 = np.sign(x) * np.absolute(x)**(1.0/5.0)
print xRoot5
#>>> [-2.40822469  1.90365394]

print xRoot5**5
#>>> [-81.  25.]

import numpy as np

y = -3.
np.sign(y) * np.absolute(y)**(1./3.)
#>>> -1.4422495703074083

>>> -3.0**(1/3)
-1.4422495703074083

>>> p = [1,0,0,3]
>>> numpy.roots(p)
[-3.0+0.j          1.5+2.59807621j  1.5-2.59807621j]

>>> import numpy as np
>>> np.cbrt(-8)
-2.0

>>> np.cbrt([-8, 27])
array([-2.,  3.])