Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3? Choose the correct option:  A) 0  B) 1  C) 2  D) 3  E) 4
For: (2^(3x+3)+3)/3   Let n = 3x + 3   2^n   2^1 = 2   2^2 = 4   2^3 = 8   2^4 = 16   2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, ....   Rule: x^(m+n) = (x^m)(x^n)   (2^(3x))(2^3)   Rule: x^(mn) = (x^m)^n   ((2^3)^x)(8) =&gt; Now, (8)(8) + 3 = (64) + 3 =&gt; and, 4 + 2 + 1 =&gt; Finally, (6 + 1)/3, and remainder is 1.   Answer: 1
<result>B</result>
Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3?