In 2 month study plan, Week 2 Day 3, Sequence Part 1, in this question, Greg converted 32 = 2^5 and later he multiplied the powers 5**32*32.* Is his allowed? because as per exponent rules a^3^3^2 is not equal to a^18 since parentheses are not there, it equals to a^19,683.
No
32^{32^{32}} = 2^{5 \cdot 2^{160}} \neq 2^{5 \cdot 32 \cdot 32}