There is no such thing. There may be useful opportunities, but it is only coincidental. It's called the Distributive Property of Multiplication over Addition - often just The Distributive Property.

\(\displaystyle 2^{5} + 2^{5} = 2^{5}(1 + 1) = 2^{5}*2 = 2^{6}\)

This seems to be to our advantage

BUT

\(\displaystyle 2^{5} + 2^{5} + 2^{5} = 2^{5}(1 + 1 + 1) = 2^{5}*3\)

This is NOT particularly to our advantage as an "exponent" rule, *per se*.

See how convenient it was in your examples that there were 2 with a 2-base and 3 with a 3-base? Very misleading.