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Multiple choice maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

Unit's digit of the number ${36^{1001}} \times$ ${7^{1002}} \times$${13^{1003}}$ is 

  1. $1$
  2. $3$
  3. $7$
  4. $8$
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D Correct answer
Explanation

Unit's digit of $36^{1001}$ will be $6$

$7^{1002}=(7^2)^{501}=(49^4)^{125}\times 49$
Unit's digit of $(49^4)$ is $1$. So, unit's digit of $(49^4)^{125}$ will be $1$ and thus, unit's digit of $7^{1002}$ will be $9$.
$13^{1003}=(13^2)^{501}\times 13=(169^4)^{125}\times 169\times 13$
Unit's digit of $169^4$ is $1$. So, unit's digit of $13^{1003}$ will be $7$.
Hence, unit's digit of $36^{1001}\times 7^{1002}\times 13^{1003}$ will be $8$.