Appending Powers Of A Row At The And Of The Same Row In Numpy Matrix

I have a numpy matrix in. I want to append the second power, third power, ..., nth power of the row to the end of the row. For instance,

my_array = [
[1,2,3],
[2,3,4],
[3,4,5],
]

If n is 3, then my_array should be the following

my_array = [
[1,2,3,1,4,9,1,8,27],
[2,3,4,4,9,16,8,27,64],
[3,4,5,9,15,25,27,64,125]
]

I can do this manually as follows: (please do not consider the dimensions below, I know they are not correct for the example)

data_poly=np.ones((209,22))

data_poly[:,0:8]=data
data_poly[:,8]=data[:,1]**2
data_poly[:,9]=data[:,2]**2
data_poly[:,10]=data[:,3]**2
data_poly[:,11]=data[:,4]**2
data_poly[:,12]=data[:,5]**2
data_poly[:,13]=data[:,6]**2
data_poly[:,14]=data[:,7]**2
data_poly[:,15]=data[:,1]**3
data_poly[:,16]=data[:,2]**3
data_poly[:,17]=data[:,3]**3
data_poly[:,18]=data[:,4]**3
data_poly[:,19]=data[:,5]**3
data_poly[:,20]=data[:,6]**3
data_poly[:,21]=data[:,7]**3

How can I automize this process?

Here is one option using broadcasting, there is probably a smarter way to reshape:

N = 3
(my_array[...,None]**(np.arange(N)+1)).swapaxes(1,2).reshape(my_array.shape[0],-1)

or using tile/repeat:

N = 3
np.tile(my_array, N)**np.repeat(np.arange(N)+1, N)

output:

array([[  1,   2,   3,   1,   4,   9,   1,   8,  27],
       [  2,   3,   4,   4,   9,  16,   8,  27,  64],
       [  3,   4,   5,   9,  16,  25,  27,  64, 125]])

input:

my_array = np.array([[1,2,3],
                     [2,3,4],
                     [3,4,5]])