What is the last digit of this number? #2222^3333#

Q. Find the last digit of #2222^3333#
I know that this is the same thing as finding the remainder when divided by 10 (mod 10). But how do we go about it?

Answer 1

The last digit will be #2#

The powers of #2# are #2,4,8,16,32,64,128,256 ....#
The last digits form the pattern, #2,4,8,6# with the same order of these four digits repeating again and again.
The powers of any number where the last digit is #2# will have the same pattern for the last digit. After a group of #4# the pattern starts again.
We need to find where #3333# falls in the pattern.
#3333div 4 = 833 1/4#
This means that the pattern has repeated #833# times followed by one number of the new pattern, which would be #2#.
#2222^3332# would end on a #6#
#2222^3333# will have #2# as the last digit.
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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