Surender,

One way to approach this problem is to write

(7 × 3)²¹ = 7²¹ × 3²¹

and then find the units digit of 7²¹ and the units digit of 3²¹ using the technique in my response to Alex's question. Multiply the two units digits obtained to find the units digit of (7 × 3)²¹ = 7²¹ × 3²¹.

For this particular problem it is easier to deal with 7 × 3 = 21 directly. Your question is to find the units digit of (7 × 3)²¹ = 21²¹.

Multiply 21 × 21. (Do it by hand without a calculator). What is the units digit?

Multiply the result of 21 × 21 by 21, again without a calculator. What is the units digit?

Multiply the result by 21. What is the units digit?

What will happen every time?

Penny