Answer:
7
Explanation:
3^0 = 1
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
3^6 = 729
3^7 = 2187
3^8 = 6581
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You can see that the pattern is beginning to repeat itself.
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So all you need do is take 2099 and divide by 3. You must pay attention to the remainder.
2099 / 4 = 524.75
The answer means that you go through the cycle 524 times getting 1,3,9,7,1 as the units digit.
In this case the remainder is 0.75 which is the same as 3/4. The remainder then is 3
If there is no remainder, the ending is a one.
if there is a remainder of 1 the answer is 3
If there is a 2 remainder, the number ends in 9
If there is a 3 remainder, the number ends in 7
And that's your answer.