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.
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Oh, dude, the units digit of 2 to the power of 2011 is 2. Because, like, when you keep multiplying 2 by itself, the units digit just keeps going 2, 4, 8, 6, and then back to 2. So, yeah, it's 2. Cool, right?
Oh, isn't that a happy little question! When we look at the pattern of units digits for powers of 2, we notice that it repeats every 4 powers. Since 2011 is 3 more than a multiple of 4, the units digit of 2 to the power of 2011 will be the same as 2 to the power of 3, which is 8.
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.
Expressed in numerical form, 248 = 281474976710656 - the units digit is therefore 6. With the exception of 20 = 1. the units digit of successive powers of 2 runs 2, 4, 8, 6... continuously - therefore, an exponent which is a multiple of 4 will have a units digit of 6.
819 = 144115188075855872 The number in the units column is therefore 2.
The last digit of a number raised to a power can be determined by finding a pattern in the units digits of the number's powers. For 2 raised to the power of 1997, the units digit will follow a pattern of 2, 4, 8, 6. Since 1997 is one less than a multiple of 4, the last digit will be 8.
Look at the first few powers of 2: 2, 4, 8, 16, 32, 64, 128, 256,512, 1024, 2048The units digit repeats every four: [ 2 - 4 - 8 - 6 ] - [ 2 - 4 - 8 - 6 ] - etc.725/4 = 181 with remainder of 1 .So if you raise 2 to the 725th power, the units digit completes the whole4-step cycle [ 2-4-8-6 ] 181 times, and then advances one more step ... to 2 .