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When the expression 3 to the 444 power plus 4 to the 333 power is written as an integer, what is the units dig?

When the expression 3 to the 444th power plus 4 to the 333th power is written as an integer, what is the units digit?

Powers of 3 are
3, 9, 27, 81, 243, …
So the units digits cycle as:
3, 9, 7, 1, and then repeat.
So 3 to the power of a number divisible by 4 (such as 444) ends in 1.
Powers of 4 are
4, 16, 64, 256, …
So the units digits cycle as:
4, 6, and then repeat.
So 4 to the power of an odd number (such as 333) ends in 4.

1+4 =
5

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