Question 321179: Which of these digits is the units digit of the number 9^99 −4^44?
A) 4 B) 3 C) 9 D) 5 E) 1
Found 2 solutions by Alan3354, toidayma:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The units digit of 99^n is
9,1,9,1,9,1...
An odd power makes it a 9.
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The units digit of 4^n is
4,6,4,6,4...
An even power makes it a 6.
9-6 = 3
Answer by toidayma(44)  (Show Source):
You can put this solution on YOUR website! In order to know the unit digit of this calculation, you have to know the digit of each number.
For 9^99, notice that 9^1 = 9, 9^2 = 81, 9^3 = ...9, and so on.
So the unit digit of 9^n with n is an odd number (99) is 9.(and if n is even, the unit digit is 1)
For 4^44, notice that 4^1 = 4, 4^2 = ..6, 4^3 = ...4, and so on.
So the unit digit of 4^n with n is an even number (44) is 6 (and if n is odd, the unit digit is 4).
Therefore, the unit digit of 9^99 - 4^44 = 9 - 6 = 3. Choose answer choice B.
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