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Whats odd numbers11/18/2023 ![]() We essentially want to find the 2013th term of the sequence above. The value of the ones digits of the powers of 2013 is as follows (starting with 2013 to the first power): In other words, the ones digits repeat every fourth power. If we multiply this by 2013, we will end up with a ones digit of 9. Notice that we are back to a ones digit with 3. To find the ones digit of 2013 to the fifth power, we will multiply 1 by 3, which gives us 3. When we mulitply 7 and 3, we get 21, which means that the ones digit of 2013 to the fourth power is 1. To find the ones digit of 2013 to the fourth power, we only need to worry about multiplying the ones digit of 2013 to the third power (which is 7) by the ones digit of 2013. ![]() When we multiply 9 and 3, we get 27, so the ones digit of 2013 to the third power is 7. In other words, 2013 to the third power will have a ones digit that is equal to the ones digit of the product of 9 (which was the ones digit of 2013 squared) and 3 (which is the ones digit of 2013). It does not matter that we do not know exactly what 2013 squared equals, beacuse we only need to worry about the ones digit, which is 9. In order to do this, we will multiply the square of 2013 by 2013. Next, we want to find the ones digit of 2013 to the third power. Thus, if we multiply 2013 by 2013, then the ones digit will be the same as. As discussed previously, if we want the ones digit of two numbers multiplied together, we just need to multiply their ones digits. To find the ones digit of the 2013 to the second power, we need to think of it as the product of 20. ![]() Let us look at the ones digit of the first few exponents of 2013. An exponent is essentially just a short hand for repeated multiplication. In short, we really only need to worry about the ones digits of the numbers we multiply when we try to find the ones digit of their product. Since the ones digit of 63 is 3, the ones digit of 137 x 219 will also be 3. For example, if we multiply 137 and 219, then the ones digit will be the same as the ones digit of. If we want to know the ones digits of the product of and, all we need to do is to look at the ones digit of the product of and. Let us say we have two numbers, and whose ones digits are and B, respectively.
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