Lets check it out: 4^17 - 2^28. The first thing to notice is that 4 = 2^2. Lets make the substitution: (2^2)^17 - 2^28. Recall the exponent law where (x^a)^b = x^ab. Lets rewire again: 2^34 - 2^28. Now, lets break this up: 2^28(2^6 - 1) = 2^28(64-1) = 2^28(63) = 2^28(9*7) = 2^28(3*3*7) = (2^28)(3^2)(7). Notice that the only prime factors of 4^17 - 2^28 are 2, 3, and 7; the greatest of which is 7.
Hope this helps. Brush up on your exponent properties !
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