(4 ^17)-(2^28)=(2^34)-(2^28)=2^28(2^6-1)=2^28*63=2^28*7*9

since largest prime number in 2^28*7*9 is 7 so answer is d

Good question - and like many exponent questions this one comes down to:

1) Finding common bases

2) Factoring common terms to turn addition/subtraction into multiplication

First, we need to get a common base of 2:

2^34 - 2^28

Then we can factor out the 2^28 term:

2^28 (2^6 - 1)

Now we know that the greatest prime factor of 2^28 is 2 (2 is its only PRIME factor), so we're left with 2^6 - 1, which is:

64-1 = 63

63 = 9*7 = 3*3*7

7 is the greatest prime factor, so the answer is D.