To find the tens place digit of (12)^(42), we need to evaluate the value of (12)^(42) first.
To calculate this, we can use the following steps:
1. Start by calculating the ones place digit of (12)^1, (12)^2, (12)^3, and so on, until we find a pattern.
(12)^1 = 12
(12)^2 = 144
(12)^3 = 1728
(12)^4 = 20736
2. Observe the pattern of the ones place digits: 2, 4, 8, 6, 2, 4, 8, 6, and so on. We notice that the ones place digits repeat every 4 powers.
3. Divide the exponent, 42, by 4: 42 รท 4 = 10 with a remainder of 2. This means that (12)^(42) can be expressed as (12)^(4 * 10 + 2).
4. Simplify the expression: (12)^(42) = (12)^(4 * 10 + 2) = ((12)^4)^10 * (12)^2.
5. Evaluate the values of (12)^4 and (12)^2:
(12)^4 = 20736
(12)^2 = 144
6. Substitute these values back into the expression:
(12)^(42) = ((12)^4)^10 * (12)^2 = 20736^10 * 144.
7. Calculate 20736^10 on a calculator or a computer to get the value. The result is a very large number, but we are only interested in the tens place digit.
8. Consider the tens place digit of the result obtained in step 7. This will be the tens place digit of (12)^(42).