Question

What is the unit digit in (3^65×6^59×7^11)

Answer 1

hi 
your question is wrong
the question is(3^65×6^59×7^71)
the answer
Any power of 6 ends with 6. 
Hence, unit's digit 6^59 = 6 

Now for powers of 3, 
Unit's digit of 3^(Multiple of 4) = 1 
Unit's digit of 3^(Multiple of 4 + 1) = 3 
Unit's digit of 3^(Multiple of 4 + 2) = 9 
Unit's digit of 3^(Multiple of 4 + 3) = 7
Hence, unit's digit of 3^65 = unit's digit of 3^(4*16 + 1) = 3 

Now for powers of 7, 
Unit's digit of 7^(Multiple of 4) = 1 
Unit's digit of 7^(Multiple of 4 + 1) = 7 
Unit's digit of 7^(Multiple of 4 + 2) = 9 
Unit's digit of 7^(Multiple of 4 + 3) = 3
Hence, unit's digit of 7^71 = unit's digit of 7^(4*17 + 3) = 3 

Hence, unit's digit of (3^65)*(6^59)*(7^71) = unit's digit of 3*6*3 = unit's digit of 54 = 4 
hope helpful