The last digit of the result of the 2008th power of 3×7×2007×13×2006 The last digit of the result of the 2008th power of 3 x the 2007th power of 7 x the 2006th power of 13

The last digit of the result of the 2008th power of 3×7×2007×13×2006 The last digit of the result of the 2008th power of 3 x the 2007th power of 7 x the 2006th power of 13

3*7=21 And the mantissa of any power of 21 is 1
So just consider the mantissa of 3*13^2006 power
That is, the mantissa of 3^2007
Note that 3^4=81 mantissa is 1
So 3^2007 mantissa is 3^(2004+3) mantissa is 3^3 mantissa is 7

Using the above method to find the last digit of the 2005th power of 2004, the 2008th power of 2007 and the 2007th power of 2008. Use the above method to find the last digit of the 2005th power of 2004, the 2008th power of 2007 and the 2007th power of 2008.

This is a pattern, without the previous tips, the latter very difficult to do.

This was a matter of finding a pattern. Without the first hint, it would be very difficult to do later.