This is unlikely to be ethical on the student's part, as it would mean them bypassing the learning expected to form part of this assessment and so they may be gaining a qualification under false pretences.
If this qualification is then used to gain a job, for example, in many locales the end result could be considered a fraudulent activity.
It is likely that the university will also have wider guidance about plagiarism. Copying from an Internet source, without acknowledgement, which the use of WolframAlpha would represent, would be considered plagiarism.
Now, it may be that the take home assessment allows the use of the Internet. In that case, using, acknowledging and citing WolframAlpha may be acceptable. At that point, whether this was a good idea would depend on how the marking scheme was constructed. If the scheme only requires the answers (and possibly working) the student may be able to get full marks. If the exam (and marking scheme) is constructed to require the student to go beyond the information available online, then the raw WolframAlpha answers would not be enough.
In practice, if the assessment was set up to be so easily solvable in this way, it is unlikely to represent best practice. A wide body of literature exists for professors on how to set assessments that also positively promote academic integrity. It may be worth the professor actively engaging with these as part of their continual staff development.