What is the digit in the unit place of 3^{99}?

Explanation

The unit digit of powers of 3 follows a cyclicity of 4: (3, 9, 7, 1). Dividing the power 99 by 4 gives a remainder of 3. Therefore, the unit digit is the 3rd number in the cycle, which is 3^3 = 27 \rightarrow 7.

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