What is the last digit of 32 power of 91? - MyTecNika

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What is the last digit of 32 power of 91?

What is the last digit of 3291?

(a) 2                (b) 4            (c) 6             (d) 8

To obtain the last digit of 32², 32³, ..., multiply the last digits i.e., 2x2, 4×2, 8x2 etc.

For 321,Last digit = 2, i.e., 2

For 322, Last digit = 2 x 2 = 4, i.e., 4

Hence, the last digit is given by:

For 32³, Last digit = 4 x 2 = 8, i.e., 8

For 324, Last digit = 8 x 2 = 16, i.e., 6

For 325, Last digit = 6 x 2 = 12, i.e., 2

For 326, Last digit = 2 x 2 = 4, i.e., 4

For 327, Last digit = 4 x 2 = 8, i.e., 8

For 328, Last digit = 8 x 2 = 16, i.e., 6

Every 4th

We can observe that the unit digit gets repeated after power of 32.

Hence, we can say that 32 has a power cycle of 2, 4, 6, 8, with frequency 4.Therefore, for powers, 1, 5, 9, 13,...., the last digit will be 2. For powers, 2, 6, 10, 14,...., the last digit will be 4.

For powers, 3, 7, 11, 15,...., the last digit will be 8.

For powers, 4, 8, 12, 16,...., the last digit will be 6.

In the question, the power is 91.

 We have to check, in which of the above series does 91 occurs.

91 is a number that gives a remainder 3 when divided by 4.

Therefore, 91 is in the series 3, 7, 11, 15...

The last digit is 8. Hence option (d).