write the following in the indicated base: 1021base three to base ten?

Another base is similar to base 10, but in the given number. So where we have ones, tens, hundreds (10 squared), thousands (10 cubed) another number system will have (using three as an example) ones, threes, nines (3 squared), twenty-sevens (3 cubed), etc.

So for 1021 it is: 1 "one"; 2 "threes"; zero "nines" and 1 "twenty sevens" for a total of 34 in base ten.