Unit digit in the expansion of 342 is:

The units digit of powers of an integer follows a repeating cycle. For 3, the cycle length is 4: the units digits of 31, 32, 33, 34 are 3, 9, 7, 1 respectively, and this block of 4 then repeats indefinitely for every subsequent set of exponents.

1. List the cycle: 31 ends in 3, 32 ends in 9, 33 ends in 7, 34 ends in 1.

2. Divide the given exponent by the cycle length: 42 ÷ 4 = 10 remainder 2.

3. A non-zero remainder r means the units digit of 342 equals the units digit of 3r. Here r = 2, so the units digit equals the units digit of 32, which is 9.

Cross-check: extending the cycle directly confirms this — 340 (exponent a multiple of 4) ends in 1, so 341 ends in 3, and 342 ends in 9, matching the remainder method above.

Hence, the units digit of 342 is 9.