We can use the laws of exponents to rewrite 4^8.869 as:
4^8.869 = 4^8 x 4^0.869
None of the answer choices match this form exactly, but we can simplify some of them to match it.
Option A can be simplified using the product rule of exponents:
4^8 x 4^85/10 x 4^9/100 = 4^8 x 4^8.5 x 4^0.09 = 4^16.59
Option B can be simplified using the power of a sum rule of exponents:
4^8+8/10+6/10+9/1000 = 4^9.025
Option C can be simplified using the sum rule of exponents:
4^8 + 4^8/10 + 4^6/100 = 4^8 x (1 + 0.1 + 0.04) = 4^8 x 1.14
Option D can be simplified using the product rule of exponents:
4^8 x 4^8/10 x 4^6/100 x 4^9/1000 = 4^8 x 4^0.8 x 4^0.06 x 4^0.009 = 4^9.869
Therefore, the answer is option D, 4^8 x 4^8/10 x 4^6/100 x 4^9/1000.