| The unit digit in the product \[{{(122)}^{173}}\] is |
A) 2
B) 4
C) 6
D) 8
Correct Answer: A
Solution :
| We know, \[{{2}^{1}}=2\] |
| \[\Rightarrow \] \[{{2}^{2}}=4\] |
| \[\Rightarrow \] \[{{2}^{3}}=6\] |
| \[\Rightarrow \] \[{{2}^{4}}=16\] |
| \[\Rightarrow \] \[{{2}^{5}}=32\] |
| \[\Rightarrow \]2 repeats at unit place after power of 4. |
| Now, \[{{(122)}^{173}}={{({{122}^{4}})}^{43}}\times 122\] |
| Unit digit in \[{{(122)}^{173}}\] |
| = Unit digit in \[{{({{122}^{4}})}^{43}}\times \]Unit digit in 122 |
| = Unit's digit in \[(6\times 2)=2\] |
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