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Solution : Let’s assume the no is 𝒙𝒚𝒛𝒏

That means n is the power where base is the three digit no. xyz.

Step 1: divide the power n by 4.

Step 2: If the remainder is 0.

If z is odd then unit digit is 1. If z is even then unit digit is 6. If z is 5 then unit digit is 5.

If remainder is 1 then unit digit will be z. If remainder is 2 then unit digit will be 𝒛𝟐. If remainder is 3 then unit digit will be 𝒛𝟑.

Example 1:-

Find the unit digit of 𝟏𝟗𝟕𝟐𝟗𝟓.

Here xyz = 197, z = 7

& n = 295

Step 1: divide 295 by 4.

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We get the remainder is 3.

Step 2: unit digit will be 𝟕𝟑 = 7×7×7 = 343 that is 3 (Answer)

Example 2:-

Find the unit digit of 𝟏𝟑𝟐𝟐𝟑𝟐.

Solution : here xyz = 132, z = 2 & n = 232.

Step 1: divide 232 by 4.

We get the remainder is 0.

Step 2: If the remainder is 0.

Check whether the z is odd, even or 5.

Step 3: z = 2 that means z is even.

So, the unit digit will be 6.

Don’t start the sum at all if you get some number like 320, 431, 535 etc.

If the z is 0, 1, 5 or 6 be sure that the unit digit will be as same as z.

Means, if z = 0, 1 , 5 or 6 unit digit will be same.

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