Analyzing the Results of Large ExponentsDate: 09/10/2007 at 22:56:52 From: Katie Subject: 1998^1998 What is 1998^1998 to the units digit? How do you solve these kind of problems? Too big a number! Date: 09/11/2007 at 11:13:10 From: Doctor Ian Subject: Re: 1998^1998 Hi Katie, A good place to start is by finding 1998^2: 1998 x 1998 ------ 1998 * 8 15984 1998 * 90 -> 179820 1998 * 900 1798200 + 1998 * 1000 + 1998000 ------------- --------- ??????4 Now, the interesting thing here is that the units digit of the product is affected ONLY by the units digits of the factors. So 1998*1998 must have the same units digit as just 8*8. Convince yourself that this is true before continuing. It would follow, then, that 1998^3 and 8^3 should have the same units digit, right? Let's check: 1998^3 = 7976023992 8^3 = 512 So really, you have a much simpler question to answer: The units digit of 8^1998 is what? That's still a big exponent, so you still need to be clever to avoid just evaluating the expression. You can do that by looking at powers of 8, and seeing if you can find a pattern in the units digit: 8^1 = 8 8^2 = 64 8^3 = 512 8^4 = 4096 8^5 = 32768 8^6 = 262144 8^7 = 2097152 and so on. Is this enough to get started? Let me know if you need more help. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 09/11/2007 at 20:43:09 From: Katie Subject: Thank you (1998^1998) Thank you very much for answering my question. You really helped me to understand that. Thanks a lot! |
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