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What digit is in the units place of the number that is 2/3 of 27^10?

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2 Answers

2/3(27^10)
2/3[(3^3)^10)]
2/3(3^30)
2(3^30)/3
2(3^29)
3^4=81
(3^4)(3^4)(3^4)(3^4)(3^4)(3^4)(3^4)(3)=3^29
3^4=81
81^7 will put a 1 in the one's place
3(81^7) will put a 3 in the one's place
now multiply by the 2 to put a 6 in the one's place
2/3(27 ^ 10 )
 
 Let's break the number to the product of the lower exponentsa
 
 2/ 3 (  27 ^ 10) =2/3 (3 ^3) ^ 10
 
              = 2/3 (3 ^ 30)  = 2/3 [(3^5 )^6]
                              
                           = 2/3 (3 ^4 * 3 ) ^6
 
                           =2/3  (2 43 ) ^6 
 
     one' digit =one's digit of 2/3( 3 ^6) =39366 
          is 6