Question

units digit in 7 powered 105  ?

Answer 1

Hi,

I will give you detailed explanation ,

So that you can solve this type of

Problem,

* The power of 7 any index repetition

7, 9 , 3 , 1 .

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1 ) 7 ^(4n + 1 ) the last digit in the

expansion is 7.

2 ) 7 ^( 4n + 2 ) the last digit in the

expansion is 9.

3 ) 7 ^( 4n + 3) the last digit in the

expansion is 3.

4 ) 7 ^(4n + 4 ) the last digit in the

expansion is 1.

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Now , let us check where our

problem fit in.

7^105 = 7 ^( 4 × 26 + 1 )

It is similar to 1) condition.

Therefore the last digit in the

expansion is 7.

I hope this will useful to you.

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