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DRDO Multi tasking staff Model paper 6

Question : 77 of 100

Marks: +1, -0

22^{471}

Solution:

The given number is

22^{471}

The unit digit of 2.

\Rightarrow 2^{1}=2

\Rightarrow 2^{2}=4

\Rightarrow 2^{3}=8

\Rightarrow 2^{4}=6

\Rightarrow 2^{5}=2

Here, the digit is repeating after every

4^{\text{th}}

power.

Now,

\Rightarrow 22^{471}=22^{468}\times 22^{3}=(22^{4})^{117}\times 22^{3}

The unit digit of expression

(22^{4})^{117}\times 22^{3}

\Rightarrow (22^{4})^{117}\times 22^{3}=6\times 2\times 2\times 2=8

Hence, the unit digit of

22^{471}=

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