Question 1208429
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Look for the repeating pattern of the last two digits of 3, 7, and 9 to increasing powers.<br>
3: 03, 09, 27, 81, 43, 29, 87, 61, 83, 49, 47, 41, 23, 69, 07, 21, 63, 89, 67, 01, 03...<br>
That pattern repeats with a cycle length of 20. 123 mod 20 = 3, so the last two digits of 3^123 is the 3rd number in the pattern: 27<br>
7: 07, 49, 43, 01, 07...<br>
That pattern repeats with a cycle length of 4. 123 mod 4 = 3, so the last two digits of 7^123 is the 3rd number in the pattern: 43<br>
9: 09, 81, 29, 61, 49, 41, 69, 21, 89, 01, 09 ...<br>
That pattern repeats with a cycle length of 10. 123 mod 10 = 3, so the last two digits of 9^123 is the 3rd number in the pattern: 29<br>
27+43+29 = 99<br>
ANSWER: 99<br>