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There is a shortcut method to solve such problems

Suppose x is raised to the power y and we need to find unit digit of .

So, we will first divide y by 4 and find the remainder thus obtained. Since on dividing and integral number by four can yield only four remainders --> 0, 1, 2 and 3.

This method applies for 4 values of x only, because for other values, you can split the values in the 4 values of x:-

x = 2, 3, 7 and 8.

For 2

====

If remainder [y/4] is 1, unit digit of = 2

If remainder is 2, unit digit of = 4

If remainder is 3, unit digit of = 8

If remainder is 0, unit digit of = 6

For 3

====

If remainder is 1, unit digit of = 3

If remainder is 2, unit digit of = 9

If remainder is 3, unit digit of = 7

If remainder is 0, unit digit of = 1

For 7

====

If remainder is 1, unit digit of = 7

If remainder is 2, unit digit of = 9

If remainder is 3, unit digit of = 3

If remainder is 0, unit digit of = 1

For 8

====

If remainder is 1, unit digit of = 8

If remainder is 2, unit digit of = 4

If remainder is 3, unit digit of = 2

If remainder is 4, unit digit of = 6

For memorising that of 3 and 7, you can check the unit digit of when 3 and 7 are raised to the power remainder [power = remainder]. For 2 and 8 this trend doesn't works.

So in your question,

Dividing 333 by 4, we get remainder 1.

So using table, when remainder is 3, unit digit of 3 [because the unit digit of 373 raised to power something is because of its original unit digit only] will be 3.

Hence unit digit of will be 3.

Hope you understood :-)

If not please comment. :-)

Suppose x is raised to the power y and we need to find unit digit of .

So, we will first divide y by 4 and find the remainder thus obtained. Since on dividing and integral number by four can yield only four remainders --> 0, 1, 2 and 3.

This method applies for 4 values of x only, because for other values, you can split the values in the 4 values of x:-

x = 2, 3, 7 and 8.

For 2

====

If remainder [y/4] is 1, unit digit of = 2

If remainder is 2, unit digit of = 4

If remainder is 3, unit digit of = 8

If remainder is 0, unit digit of = 6

For 3

====

If remainder is 1, unit digit of = 3

If remainder is 2, unit digit of = 9

If remainder is 3, unit digit of = 7

If remainder is 0, unit digit of = 1

For 7

====

If remainder is 1, unit digit of = 7

If remainder is 2, unit digit of = 9

If remainder is 3, unit digit of = 3

If remainder is 0, unit digit of = 1

For 8

====

If remainder is 1, unit digit of = 8

If remainder is 2, unit digit of = 4

If remainder is 3, unit digit of = 2

If remainder is 4, unit digit of = 6

For memorising that of 3 and 7, you can check the unit digit of when 3 and 7 are raised to the power remainder [power = remainder]. For 2 and 8 this trend doesn't works.

So in your question,

Dividing 333 by 4, we get remainder 1.

So using table, when remainder is 3, unit digit of 3 [because the unit digit of 373 raised to power something is because of its original unit digit only] will be 3.

Hence unit digit of will be 3.

Hope you understood :-)

If not please comment. :-)