Question

The unit digit of 7651^496-9875^576 is
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Answer 1

Answer:

units digit is 1.

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Answer 2

The unit digit of the given number is 6.

Given:

The expression $7651^{496} - 9875^{576}$

To find:

Unit digit of the resultant number

Solution:

First number = $7651^{496}$

Unit digit of base = 1

⇒ Unit digit of 7651ⁿ = 1

[∵ The power of any number with unit digit 1 is 1]

⇒ Unit digit of $7651^{496}$ = 1 [i]

Now,

Second number = $9875^{576}$

Unit digit of base = 5

⇒ Unit digit of 9875ⁿ = 5

[∵ Power of any number with unit digit 5 is 5]

⇒ Unit digit of $9875^{576}$ = 5 [ii]

⇒ From i and ii,

Unit digit of $7651^{496} - 9875^{576}$ = xxx1 - yyy5 = 6

∴ Unit digit of required number is 6.

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