CAS and exponents issues

[sasa]

The CAS in theory should mimic human behavior in solving math problems, in this case expressions. In upper particular cases, that is not consistent.

For instance:
\(2^{100} \cdot 2^{200} + 9^{1/5}=9^{1/5} + 203703...\)
\(2^{100} \cdot 2^{200} \cdot 9^{1/5}=203703...\cdot 9^{1/5} \)

WolframApha return results in the same manners, except it handles \(9^{1/5}\) correctly, which indicates that problem is in the CAS, or missing appropriate settings.

Multiplication issue with the same exponent is specific to the Prime.
The \(3^{2/5}=(3^{1/5})^2\) is also specific to the Prime.
Etc...