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BlakeTo find the units digit of 3 to the 200th power, we need to observe the pattern of units digits as we raise 3 to higher powers. The units digit of 3 to any power follows a repeating cycle: 3, 9, 7, 1. Since the cycle has a length of 4, we can divide 200 by 4 to find the remainder. 200 divided by 4 gives a remainder of 0, meaning the units digit of 3 to the 200th power is the last digit in the cycle, which is 1.
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What is the units digit of 3 to the power of 19?
it is 3
What is the units digit of 3 to the 84th power?
7
What is the units digit of 2013 to the power of 2013?
Oh, dude, okay, so when you raise 2013 to the power of 2013, you're basically asking what the units digit of that massive number is. Well, lucky for you, you don't need to calculate the whole thing because the units digit of a number repeats in a pattern. So, the units digit of 2013 to the power of 2013 is 7. Cool, right?
What is the units digit of 27 to the 27th power?
To find the units digit of (27^{27}), we can look at the units digit of (27), which is (7). We then need to find the units digit of (7^{27}). The units digits of the powers of (7) cycle every four terms: (7^1 = 7), (7^2 = 49) (units digit (9)), (7^3 = 343) (units digit (3)), and (7^4 = 2401) (units digit (1)). Since (27 \mod 4 = 3), the units digit of (7^{27}) is the same as that of (7^3), which is (3). Thus, the units digit of (27^{27}) is (3).
What is the unit digit of 3 to the 60 power?
Well, honey, to find the unit digit of 3 to the 60th power, you just need to look for a pattern. The unit digits of powers of 3 repeat every 4 powers, so you divide 60 by 4, which gives you a remainder of 0. Therefore, the unit digit of 3 to the 60th power is 1.
