Hi sud21,
These types of questions are essentially about 're-organizing' the information (in this case, by factoring and using exponent rules).
We start with
5^8 + 10^6 - 50^3
We can leave the first term 'as is' and re-write the second and third 'terms'...
5^8 + (2^6)(5^6) - (2^3)(5^3)(5^3) =
5^8 + (2^6)(5^6) - (2^3)(5^6)
Next, we can factor 5^6 out of each term....
(5^6)[5^2 + 2^6 - 2^3]
Since the terms in the bracket are relatively small, we can calculate and simplify...
(5^6)[25 + 64 - 8]
(5^6)[81]
The 81 can be rewritten....
(5^6)[3^4]
Thus, the smallest prime factor is 3...
Final Answer: B
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5� + 10� - 50³ =
5� * (5² + 2� - 2³) =
5� * (25 + 64 - 8) =
5� * 81 =
5� * 3�
5� * (5² + 2� - 2³) =
5� * (25 + 64 - 8) =
5� * 81 =
5� * 3�
