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

Question

Help... I am so confused with this problem. 

Answer 1

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

Answer 2

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