mind that 7^6^5 and 7^6^21 is different, see the pattern from 0 to 8 better than just 0-4

Yes, the last digit of 6^21 is a 6. You have that part right. However, that doesn't mean that 7^(6^21) has the same last digit as 7^6.

An easy way to see this is to look at smaller numbers, where 2^6 = 64, and 2^16 = 65,536. Both exponents end with 6 ("are
congruent, modulo 10") but the powers don't end with the same digit.

No answer, no example, no issue.

What do you mean it is not catching the error? You are probably throwing an error when you should not. In general it doesn't matter which kind of error throw, the tests only control an error is thrown when it should be. I cannot say more because I haven't solved the kata, but this seems very light to raise an issue. You must provide clear examples of bad tests according to you.

it can be any kind of error that you've encountered in the past

wdym raising an error is not catching the error?

https://www.wolframalpha.com/input?i=7%5E6%5E21

Your logic is not 100% correct. For this test case, last digit should be 1.
Not a kata issue.