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).