Question

find the last digit of 3278 to the power 123​

Answer 1

Answer:

the last digit will be odd

Explanation:

for example- 123× 123×123 when its unit place is multiplied the number will be 27 and the unit place of 27 is 7.

FINAL ANSWER- odd

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Answer 2

Answer:

As per the data given in the above question.

we have to find the unit place of (3278)¹²³

Always know that the units digits go in patterns of 4 in indices, and they always depend on the units digits of the original number i.e. the base (3278 here).

So here, the unit digit is 8 and the pattern is:

$For 8^1, unit digit = 8$

$For \: {8}^{2} , unit \: digit = 4 \: (8^2 is 64)$

$For \: 8^3, unit digit = 2(8^3 is \: 512)$

$For 8^4, unit digit = 6 (8^4 is 4096)$

Now, lets see the index of the given number: 123

$\frac{123}{4} = 30 \: with \: remainder \: 3$

This means that there are 30 complete sets of 4, with remainder 3.

As we saw, 8³=512, so (3278)¹²³ will have unit digit as 2.

Hence ,(3278)¹²³= 2 will be at unit place .