SOLUTION: 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
Algebra.Com
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.
---------------------------
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.
RELATED QUESTIONS
For every positive 2-digit number, x, with tens digit t and units digit u, let y be the... (answered by Fombitz)
For every positive 2-digit number, x, with tens digit t and units digit u, let y be the... (answered by Fombitz)
Which of these numbers is the units digit of the number 2^l00 + 1 ?
A) 2 B) 5 C) 9 D)... (answered by Alan3354)
What is the units digit of 3^2009?
(a) 1 (b) 3 (c) 5 (d) 7 (e) 9
(answered by richwmiller,scott8148)
What is the units digit of 3^35?
a 1 b 3 c 5 d 7 e 9
(answered by Theo)
If n is a positive integer, which of the following cannot be the units digit of 7^n?... (answered by Alan3354)
If n is a positive integer, which of the following cannot be the units digit of 7^n ?... (answered by JBarnum)
which of the following could be the units digit of 57^n where n is a positive integer?... (answered by richard1234)
The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible
even... (answered by Edwin McCravy)