'54^35' will end in the digit '4' because '35' is an odd number, and the last digit of any number whose last digit it is '4' will be '4' if this number is multiplied by itself and odd number of times, and '6' if it is multiplied by itself an even number of times.
'28^21' will end in digit '8'; the pattern is a little more complicated than with ending digit '4', so I will cut the explanation and just say the last digit pattern is '8', '4', '2', '6', repeat (e.g. 8, 64, 512, 4096, 32768, etc.). This means '28^21' will end in digit '8' (following the pattern).
So, all that is left to do is add '4' and '8', which gives 12. The last digit of '54^35+28^21' is 2.