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I guess you mean what's the units digit of 32011.
It is 7.
To work this out, see how the units digit of 3n changes; it goes:
3, 9, 7, 1, 3, 9, 7, 1, ...
(only the first 8 powers are shown) repeating the same sequence of 4 digits. So if we find the remainder of 2011 divided by 4, it will tell us which of the four numbers (3, 9, 7, 1) will be the units digit of 32011:
2011 ÷ 4 ⇒ remainder 3, so the 3rd digit is the required digit: 7.
(If there had been no remainder, then the 4th digit, namely 1, would have been the required value.)
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What is the units digit of 2 to the power of 2011?
To find the units digit of a number raised to a power, we can look for patterns in the units digits of the powers of that number. For 2, the units digits of the powers cycle in a pattern: 2, 4, 8, 6. Since 2011 is 3 more than a multiple of 4 (2011 = 4 * 502 + 3), the units digit of 2 to the power of 2011 will be the fourth number in the cycle, which is 6.
What is the units digit of 7 to the 15 power?
Power 2: units digit 9. Multiply by 49 again to get power 4: units digit 1. So every 4th power gives units digit 1. So 16th power has units digit 1, so the previous power, the 15th must have units digit 3.
What is the units digit of 3 to the 53rd power?
3
What is the units' digit of 3 to the 333?
To find the units' digit of 3 to the power of 333, we need to look for a pattern. The units' digit of powers of 3 cycles in a pattern: 3, 9, 7, 1. Since 333 divided by 4 leaves a remainder of 1, the units' digit of 3 to the power of 333 will be the first digit in the pattern, which is 3.
What is the units digit of the 5857th triangular number?
3
