Exponential Quaternions not working

Questions
1

I can successfully add and multiply quaternions, but I can’t figure out how to raise to the power of a quaternion? Advice?

In my case, this works:

Needs["Quaternions`"]
Needs["Quaternions`"]
NumberForm[
 N[(Quaternion[0, 0, 0, 1] + 
       Quaternion[0, 0, 0, -1/(n + t)])^(n + t), 5]

But this does not work:

Needs["Quaternions`"]
NumberForm[
 N[(Quaternion[0, 0, 0, 1] + 
       Quaternion[0, 0, 0, -1/(n + t)])^(Quaternion[0, 0, 0, 1]**(n + t)), 5]

Suggestions?

2

Maybe:

Needs["Quaternions`"]

n = 1; t = 2;
(Quaternion[0, 0, 0, 1] + Quaternion[0, 0, 0, -1/(n + t)])^(n + t)

(*Quaternion[0, 0, 0, -(8/27)]*)
3

The Wolfram Quaternions package supports raising a quaternion to a real number, but not to another quaternion.

Needs@"Quaternions`"

In[2]:= Quaternion[1, 2, 3, 4]^5
Out[2]= Quaternion[3916, 1112, 1668, 2224]

In[3]:= Quaternion[1, 2, 3, 4]^Quaternion[5, 6, 7, 8]
Out[3]= Quaternion[1, 2, 3, 4]^Quaternion[5, 6, 7, 8]
4

I see. That’s too bad. Do you know of any alternative program I could use?

Thanks for the reply.

5

I have not come across any program where this can be done.

And, if it could be done, what is achieved? What would be the meaning of \text{quaternion}^{\text{quaternion}} ?