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?
7
To 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.
3 to a power divisible by 4 will have a units digit of 1.The powers of 3 are 3, 9, 27, 81 ... obviously, the next one will have a units digit of 1x3 or 3, the next one will have a units digit of 3x3 or 9, the next one will have a units digit of 7 (because 9x3 is 27), the next one will have a units digit of 1 (because 7x3 is 21), and then the cycle starts over with a units digit of 3 again.
Its positional place value is seven ones or units = 7
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?
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.
7
When multiplying numbers with the same units digit, the units digit of the product is determined by the units digit of the base number raised to the power of the number of times it is being multiplied. In this case, since 7 is being multiplied 100 times, the units digit of the product will be the same as the units digit of 7^100. The units digit of 7^100 can be found by looking for a pattern in the units digits of powers of 7: 7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401, and so on. The pattern repeats every 4 powers, so the units digit of 7^100 will be the same as 7^4, which is 1. Therefore, the units digit of the product when one hundred 7's are multiplied is 1.
To 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.
3 to a power divisible by 4 will have a units digit of 1.The powers of 3 are 3, 9, 27, 81 ... obviously, the next one will have a units digit of 1x3 or 3, the next one will have a units digit of 3x3 or 9, the next one will have a units digit of 7 (because 9x3 is 27), the next one will have a units digit of 1 (because 7x3 is 21), and then the cycle starts over with a units digit of 3 again.
The digit in the units column of the number 7157 is 7.
Well, isn't that a happy little math problem! When we look at the unit digit of powers of numbers, we focus on the cyclical pattern they follow. The unit digit of 3 raised to any power follows a pattern: 3, 9, 7, 1, and then repeats. So, to find the unit digit of 3 to the power of 34 factorial, we look for the remainder when 34 factorial is divided by 4, which is 2. Therefore, the unit digit of 3 to the power of 34 factorial is 9.
7 7 7 7
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.)
Its positional place value is seven ones or units = 7
It is the digit 7 that is in the ones or units place