Determine the ones' digit when the 14 to the power of 101 expression is evaluated.?

Answer 1

the ones' digit when a number beginning with 4, such as14^( an even number) will always be 6
and that of 14^( an odd number) will always be 4.
so to your question, the answer is 4

Answer 2

The last digit of the number 14 to a power (or 4 or 24, etc.) follows the sequence 4 - 8 - 6 - 2 - 4... The last digit repeats every 4 times.

14^101 MOD 10 = 14^1 MOD 10 which equals 4.

Answer 3

As 14 is raised to successive powers, the ones digit will alternate between 4 and 6: if the previous power is 4 in the last digit, new last digit will be 6 and vice versa. The even powers will be 6, the odd, 4, so 14 to the power of 101 will be 4.

Answer 4

For a slightly more formal treatment of this. The question can be restated as

find 14^101 mod 10.

Since the final digit of any positive integer is that integer mod 10.

14 = 4 mod 10

14 ^ 101 = 4 ^ 101 mod 10
= 4 mod 10 by the prior arguments

On a side note they should implement tex on here to make writing math easy

Answer 5

Well, first of all, the ones' digit of the result will be completely dependent on the ones' digit of 14 -- in other words, 4.

Notice the pattern in the ones' digit as I take 4 to various powers:

4¹ = 4 -- ones' digit is 4
4² = 16 -- ones' digit is 6
4³ = 64 -- ones' digit is 4
4^4 = 256 -- ones' digit is 6
4^5 = 1024 -- ones' digit is 4

See the pattern? If the power is odd, the last digit is 4, but if the power is even, the last digit is 6.

So, based on that, I think you can work out the answer. :-) Hope that helps!

Answer 6

If you investigate this, you will find that the one's digit alternates between 4 and 6. Since 101 is odd, the digit will be 4.

Answer 7

14^1 = 14.
14^2 = 196.
14^3 = 2744.

The one's digit for powers of 14 will be 4 for odd powers, or 6 for even powers.

14^101 will have a one's digit of 4.

Answer 8

it will be 4